The chief NATO commander in Europe, U.S. Army Gen. Bernard Rogers, is expected to deliver secret new proposals later this month to Greece and Turkey in an effort to end the lingering feud between the two nations and bring Greece back into the NATO military alliance.

Rogers' mission comes at a time when officials here and abroad feel the Greek-Turkish split has reached a potential turning point which could provide the best opportunity for solving the dispute that has seriously weakened NATO's southeastern flank for the past six years.

One key factor is that 1981 is an election year in Greece. The conservative government of Prime Minister George Rallis is said to believe it would be best to get the NATO question resolved before that election rather than go into it with such an emotional and controversial issue left hanging.

The Athens government, sources say, is now bringing heavy pressure on the United States and the rest of the alliance to resolve remaining Turkish objections and get the question of Greece's reintegration into NATO settled by the end of this year at the latest.

The Sunday Times of London reported from Athens last week that Greek Foreign Minister Constantine Mitsotakis told the U.S. ambassador to Greece, Robert McCloskey, that if there was no deal on full Greek reintegration into NATO by autumn, the Greek government would ask Washington to dismantle U.S. military bases in Greece.

McCloskey is now in the United States on leave, and sources close to him say no such ultimatums were given by the foreign minister or in subsequent meetings between McCloskey and the prime minister.

But they describe Athens' new push to get back into NATO as the most serious and determined in several years and acknowledge that failure to resolve the NATO problem poses at least an indirect threat to the continued operation of four important U.S. military facilities on the Greek mainland and the Greek island of Crete.

The Greeks, bitter and frustrated over their inability to halt the Turkish invasion of Cyprus or to get the United States or NATO to stop it, pulled out of the military wing of the alliance in 1974. Athens, however, retained its ties to the political structure of the 15-nation North Atlantic Treaty Organization.

Beginning in 1976, Greece began pressing for reinstatement in the military command. But the Turks have been essentially vetoing this, with the main sticking point being the question of how control of the airspace over the Aegean Sea and the continental shelf under that sea is handled.

In February, Greece rejected an earlier NATO plan for shared control. The Greeks, essentially, want to go back to the pre-1974 arrangements in the Aegean.

Details of Rogers' new proposals are being very closely held by the general. In fact, discussions with some officials here reveal a hint of annoyance that they may be too closely held and therefore somehow not get the full benefit of help from the diplomatic specialists.

Rogers, however, is said to have a mandate from NATO secretary general Joseph Luns to press ahead and has already held preliminary discussions with middle-level Greek officials on the new formula, which U.S. officials say they believe Greece is prepared to accept.

In June, Foreign Minister Mitsotakis told foreign reporters that if Greece does not succeed in its quest to reenter NATO, "the pursuit of a solution on the American bases will become much more difficult. And I am sure the Americans are aware of this." He said the government didn't want to link those two issues, "absolutely" but pointed out that the NATO negotiations would certainly be an important factor in the ultimate fate of the U.S. bases.

The key U.S. bases include a Navy logistics support facility for the Sixth Fleet at Suda Bay on Crete and an Air Force communications station at Nea Makri on the mainland and an Air Force facility at the Hellenikon airfield outside Athens.

The use of these facilities goes back to a 195o bilateral agreement with Greece, and these installations have been allowed to continue operating through the lingering post-Cyprus NATO crisis. A new arrangement in 1977 was initialed but never signed by the two governments.

Meanwhile, events in the Persian Gulf and Afghanistan have made the Greek installations more important to the United States as possible support for any rapid deployment force sent in to the region. And the absence of the Greek navy and air force from NATO's integrated command, plus the feud with neighboring Turkey, has also become of even more concern because of those same events.

U.S. officials say that if the Rogers plan fails, the Greeks have suggested privately that they would then have to reconsider their entire effort to rejoin the military alliance. They say, however, that Greece, to the best of their knowledge, has not threatened to sever its political ties to NATO.

The U.S. hope is that even in the event of failure, Greece would negotiate a separate new U.S. base arrangement as an outgrowth of their common membership in NATO.

Late last month, Secretary of State Edmund S. Muskie, after meeting separately with Greek and Turkish foreign ministers, had some optimistic words for reporters at the NATO meeting in Ankara, Turkey.

Muskie and Greece seemed "agreeable" to moving forward with both the NATO reintegration and a new U.S. base agreement.

Other officials point out that Muskie and both foreign ministers are relatively new in their jobs and haven't gone through the acrimony that Greek-Turkish negotiations almost always involve at the crucial point.