Pola Negri, a tempestuous green-eyed vamp of the silent screen who tantalized audiences with her on- and off-camera romances, died Saturday at Northeast Baptist Hospital in San Antonio. She was 88 years old and lived in San Antonio.

Miss Negri was admitted to the hospital with pneumonia last week, hospital officials said yesterday. Her physician, Dr. Houston Wade, said she had been diagnosed two years ago as having a brain tumor. She decided not to undergo treatment, he said.

There were believed to be no survivors. ---- Most Exotic of Stars

The 1920's and 30's were the Age of the Vamp in the movies, and of all the screen vamps, Pola Negri was, unquestionably, the most colorful, the most exotic, the most mysterious.

The Polish-born Miss Negri was a startlingly beautiful woman, with skin as delicately white as fine porcelain, jet black hair and flashing dark-green eyes.

Her off-screen life was more tempestuous than any role she ever played and, although she often insisted that she wished only to be left alone, she could shrewdly maneuver her love affairs and feuds into avalanches of personal publicity.

Men found her fascinating. She married two noblemen and divorced both. She was the mistress and fiancee of Charles Chaplin, whom she jilted in a whirl of headlines. She was living openly with Rudolph Valentino, the romantic idol of millions of women the world over, at the time of his death in 1926. And Adolf Hitler was so taken with her that he personally intervened to countermand an order, issued by the Nazis on the ground that they thought Miss Negri was part-Jewish, forbidding her to work in Germany.

The temperamental star flourished in the long-gone era of the flamboyant screen siren, competing for roles and popularity with such other stars as Gloria Swanson and Theda Bara. Festooned in Diamonds

Whenever she appeared in public, she was festooned in diamonds and pearl brooches from her $1 million collection, acquired cut-rate from Hapsburgs and Hohenzollerns who could no longer afford them. She popularized painted toenails in the mid-20's, and when she took to wearing turbans, or appeared in high boots, thousands of American women slavishly copied her.

She maintained a mansion in Beverly Hills, a villa on the Riviera and a chateau north of Paris, and just before the crash of 1929 her personal fortune was estimated at $5 million. She lost most of her money and possessions, however, and spent her last years living in elegant simplicity in San Antonio.

In ''Memoirs of a Star,'' published in 1970, Miss Negri wrote that she was born in Lipno, Poland, on New Year's Eve, 1899. (Other sources, however, give the date as three to five years earlier.) Her mother was the former Eleanora de Kielczeska, from a family of impoverished nobility; her father was Jerzy Mathias-Chalupec, a Slovak immigrant.

Miss Negri's two sisters died in childhood. Her father was arrested by Czarist troops in 1905 for revolutionary activity in what was then Russian Poland. He was sent to prison and, although he was ultimately released, he did not return to his wife and daughter.

Miss Negri's mother had to go to work as a cook to maintain a one-room apartment in a Warsaw slum and earn enough money to send Pola to the Imperial Ballet School. Pola's first public performance was in the role of a cygnet in ''Swan Lake,'' with the Imperial Ballet. Illness Ended Dance Career

Her dancing career ended when she was 13 years old, however, because she contracted tuberculosis and had to be sent to a sanitarium. Pronounced cured a year later, she returned to Warsaw and was admitted for study at the Imperial Academy of Dramatic Arts after falsely stating she was 17. It was at that time that she adopted her stage name - Pola, the diminutive of her given name, Apolonia, and Negri, after Ada Negri, an Italian poet whom she admired.

She was one of Poland's leading actresses when she was 17, at which time she made her first movie, a two-reeler called ''Slaves of Sin.'' In 1918 she went to Berlin to perform a leading role in Max Reinhardt's pantomime ''Sumurun,'' which was later filmed as her third full-length movie.

Miss Negri's roles in her first two pictures, ''The Eyes of the Mummy Ma'' and ''Carmen,'' typed her as the man-ruining vamp. She took time out from her career in 1919 to be the wife, briefly, of Count Eugene Dambski, a Polish army career officer, then returned to Berlin to make films. ''Madame Du Barry,'' released in the United States under the title ''Passion,'' won her a Paramount Pictures contract and she was brought here in 1922.

During the Atlantic crossing, Miss Negri's agent scolded her for spending most of her time in her cabin. ''Make a few appearances,'' he said. ''Think of the publicity.''

''I am thinking of it,'' she replied. ''We will get more publicity this way. I have already learned that the fewer appearances you make, the more they will talk about you. All you have to do is to say you want to be alone - and the whole world thinks you are exotic and glamorous. It never occurs to them that you are simply tired.'' Feud With Swanson

In Hollywood, while carefully limiting her public appearances, Miss Negri, with equal assiduity, cultivated several headlined feuds, most notably with Gloria Swanson, her rival at Paramount. (The leading ladies once had a cat fight using real cats.) Miss Negri's Hollywood films were not artistic landmarks, but most were extremely successful at the box office. Among them were ''Belle Donna'' (1923), her first American movie; ''The Cheat'' (1923); ''Men'' (1924); ''The Spanish Dancer'' (1923); ''Shadows of Paris'' (1924); ''East of Suez'' (1925) and ''Forbidden Paradise'' (1924). At the height of her popularity, she was so much in demand that she ground out five pictures in a single year.

However, she always seemed able to find time for romance. Her first big headlined Hollywood affair was with Charlie Chaplin, who in 1964 wrote in his autobiography that the relationship was essentially one of the pursued (Chaplin) and the pursuer (Negri). In her own memoirs Miss Negri observed tartly:

''A great deal has been written about my relationship with Charlie Chaplin. Unfortunately, much of it has been written by Mr. Chaplin. Still less fortunately, what he wrote was largely untrue. Rather than say he behaved in less than a gentlemanly fashion, I would prefer to excuse him on the grounds that all clowns live in a world of fantasy.''

Miss Negri went on to say that her relationship with Mr. Chaplin had been intimate and stormy, that he was an inept lover, that he proposed marriage and that finally she ended the affair, over Mr. Chaplin's tearful entreaties. Her Greatest Love

According to Miss Negri, the greatest love of her life was Rudolph Valentino. On their second meeting, she wrote in her memoirs, she found him so passionately overpowering that on that very night they became lovers and remained so for nearly a year, until his death in 1926.

Valentino, called by his adoring public ''The Great Lover,'' was indeed the great lover, she wrote, capable of making such romantic gestures as sprinkling rose petals on the bed before they retired. He could also be quite prosaic. For example, he often wept because he was losing his hair, and sometimes the sex symbol of American women preferred making spaghetti for Miss Negri to making love to her.

After collapsing at Valentino's funeral in New York, Miss Negri took his body back to California by train, stopping at dozens of stations along the way so that hysterical Valentino-worshipers could pay him tribute. She was accused of using the cortege to garner personal publicity, and, true or not, soon afterward her popularity at the box office waned. When her contract came up for renewal, she found she was no longer wanted at Paramount.

Her standing with the Valentino cult was forever shattered when, in 1927, less than a year after Valentino's death, Miss Negri was married to Serge Mdivani, an impecunious Georgian prince, and took him to live in her chateau in France. They were divorced in 1931, after Miss Negri had lost the bulk of her fortune through, she later wrote, her husband's mismanagement of her affairs during the stock-market crisis. Went to Berlin in 1935

After the indifferent reception to her first talkie, ''A Woman Commands,'' Miss Negri in 1935 fled Hollywood for Berlin, where she made pictures until the outbreak of World War II. For a time she was prohibited from working by Joseph Goebbels, the Nazi propaganda minister, who put her name on a list of suspected ''non-Aryans.''

Hitler, who was said to be so fond of her German-made movie about mother love, ''Mazurka,'' that he had it run weekly so he could have a good cry, personally overruled Goebbels. Shortly after, newspapers in Europe and the United States printed reports of a romance between Hitler and Miss Negri. She sued the French magazine that initiated the reports and won a 10,000-franc judgment.

Miss Negri, who was living on the Riviera when Germany invaded France, returned to the United States in 1941. Two years later she played a featured comedy role in ''Hi Diddle Diddle,'' but no other film offers were forthcoming.

By the end of the war, she was reduced to living in one room in a small hotel in New York and selling off her jewelry to survive. Ultimately, she recovered some money and property tied up in Europe during the war.

From 1948 to 1963, Miss Negri lived in California and Texas with Margaret L. West, who bequeathed her property in San Antonio. In recent years Miss Negri lived in a duplex apartment in San Antonio, attended by a maid, a chauffeur and a secretary.

Miss Negri made her last attempted comeback in ''The Moonspinners,'' a Walt Disney film released in 1964. As production on the movie began in London in 1963, she proved she had not lost her knack for finding a bizarre gimmick sure to give her headlines. For her first press conference, she entered the room with a frisky cheetah on a leash.