Reports that Oman will permit the United States to set up a military base here has become the source of potential new tensions between the sultanate and its neighbor, the Marxist nation of South Yemen.

The story, in various versions with different embellishemnts, has been bouncing around newspapers in Europe for weeks. Moscow Radio has reported it as a fact.

In its general form, the story is that the U.S. Navy, or perhaps the air force, or maybe both, will take over an air base on the Omani island of Masirah when it is evacuated by Britain's air force in March and make it the center of an enlarged American military presence in the Persian Gulf and Indian Ocean.

One theory is that U.S. is looking for an alternative to the three-ship naval base it maintains in Bahrain and is expected to give up this year or next.

According to Moscow Radio, Masirah would be a link in "a chain of American bases running from Japan through the Philippines to Diego Garcia," the Indian Ocean atoll where the Navy has communications facilities and the Pentagon wants to expand.

The prime minister of South Yemen, Ali Nasser Mohammed, told a Kuwati newspaper last week that a decision by the sultan of Oman to allow an American base on Masirah would be "an act of treason against the Arab peoples." He said it would mean "American dominance not only of the Arab seas but of the whole Arab world and its wealth."

According to Sultan Qaboos Bin Said, however, the Soviets and their allies in Aden are attacking a straw man.

"There is no truth in it," he said in an interview. "We have no agreement with the Americans to inherit that base. It will be a training center for our air force and a third airport for Oman."

He said that if the U.S. or "any friend" asks for transit rights or refueling facilities on Masirah, "we are disposed to grant it," but Oman has "no intention" of allowing the establishment of any permanent foreign military installation there.

According to informed sources here, the possibility of U.S. use of Masirah was discussed when the British first announced their intention to withdraw, but both sides agreed that he outcry against such an arrangement in Washington and elsewhere in the Arab world would be politically embarrassing.

South Yemen supported a guerilla insurgency against the sultan's rule in Oman's southern province of Dhofar. Although that war is over, relations between the two countries remain strained. One issue is the continued presence in Oman of a brigade of Iranian troops sent across the gulf by the strongly anti-Communist shah of Iran to help the sultan put down the insurgency.

American embassy officials declined to comment on the reports about Masirah Island. Analysts pointed out, however, that it has been U.S. policy for the past few years to equip friendly regional powers like Iran and Saudi Arabia so that they can assume defense and security responsibilities, rather than to get involved directly.