The Carter administration is planning a significant cut in the size of the U.S. military force on Taiwan in the next four months, according to American servicemen on the island - a step that is seen as a signal of U.S. interest in closer relations with Peking.

American servicemen on Taiwan say they have been told the 1,000-member U.S. military contingent on this nationalist Chinese-held island will probably be reduced by about 400 persons by Oct. 1, an acceleration of the pace of withdrawal under the Carter administration.

A U.S. military spokesman said there would be staff reductions but he did not know of any cut that large or that soon.

Any major acceleration of the pace of U.S. military reductions here would come on the heels of White House national security adviser Zbigniew Brzezinski's recent visit to Peking.

Brzezinski strongly endorsed normalization of relations with Peking during the trip. He also made several statements sharply critical of the Soviet Union that appeared to signal his interest in using stronger ties with Peking to counter Soviet moves in Africa and elsewhere.

The United States promised China under the terms of the 1972 Shanghai communique - agreed upon during the peak of the Vietnam war when there were about 10,000 U.S. servicemen on Taiwan - that it would progressively reduce its forces on the island.

By the beginning of the Carter administration, the U.S. force here was down to about 1,300, but in the last 16 months only about 300 additional servicemen have been removed from Taiwan, according to official figures.

Servicemen Taiwan say an unusual number of enlisted men and officers have been told recently they will be leaving in the next few months, before their normal rotation dates. Co-workers have been told there will be fewer replacements and that their units, mostly engaged in communications, maintenance, housekeeping and entertainment work, must get with smaller staffs.

Nay Lt. Comd. Paul W. Hanley, spokesman for the U.S. Taiwan Defense Command, said he had heard of no deadlines for future staff reductions.

"The best way to think of this is a gradual decrease which has been going on for five years and is continuing to go on," he said."Right now all the future holds is continued reduction. Right now it is about 1,000 and you can project it out as far as you want."

The International Communication Agency, formerly the U.S. Information Service, has announced the closing of two U.S. libraries that have served Taiwanese living in the cities of Tainan and Taichung. A spokesman for the agency in Taipei said budget cuts forced the closings. When asked if Washington's relations with Peking had any impact on the decision, he said, "All factors were considered."

The U.S. government has rarely made any formal announcements of its successive military reductions on Taiwan. Servicemen on the island say those privy to personnel plans report that a 40 per cent reduction is tentatively scheduled for Oct. 1, but they do not know if that plan is final.

"Several army people have come in and said, "Pack your bags, you're leaving," said one serviceman. They say they have been told by officers not to discuss their sudden transfers. "Instead a lot of people say things like," we've decided not to buy that car after all," one said.

One serviceman said the reported Oct. 1 deadline for a reduction seemed as insulting to the Taiwan government as Brzezinski's decision to visit Peking just as the new Taiwan President, Chiang Ching-Kuo, was being sworn in. "Why don't they just wait a few days and do it by double ten?" said the serviceman, referring to Taiwan's Oct. 10 national day celebration.

In the Shanghai communique negotiated by President Nixon and Chinese Premier Chou En-lai, the United States said "it reaffirms its interest in a peaceful settlement of the Taiwan question by the Chinese themselves. With this prospect in mind, it affirms the ultimate objective of the withdrawal of all U.S. forces and military installations from Taiwan. In the meantime, it will progressively reduce its forces and military installations on Taiwan as the tension in the area diminishes."

Peking has demanded that Washington withdraw all military forces, close its embassy and abrogate its defense treaty with Taiwan before Peking will agree tll diplomatic relations. U.S. officials are reluctant to to do this without some sort of guarantee that China will not try to conquer the island by force once Washington has severed its formal relations with the island.

There have been no American combat units on the island since 1975, but Taiwan's half million active duty troops are thought to be well trained and there is a much larger ready reserve.China has more aircraft and submarines than Taiwan, but its surface navy remains inferior for what could be intense fighting in the Taiwan Strait.