Secretary of State Alexander M. Haig Jr. said today he may return to the Middle East within a few weeks to present Israeli and Egyptian leaders with U.S. ideas for concluding an agreement on self-rule for the Palestinian inhabitants of Israeli-occupied territories.

Following a meeting with Israeli Prime Minister Menachem Begin, Haig said that a new trip to the region was likely by "me personally or at least a representative" to advise Egypt and Israel of his views on how to achieve a breakthrough in the autonomy negotiations between the two countries.

Reports were circulating here tonight that when Haig returns to Washington Friday, his assistant secretary for Middle East affairs, Nicholas Veliotes, will remain behind and go to Jordan for talks with King Hussein. Although U.S. officials refused to comment, there was speculation that such a trip might involve a new attempt to persuade Hussein to end his boycott of the autonomy talks.

A more likely explanation is that Veliotes would talk with Hussein about the resolution introduced by Jordan in the United Nations Security Council, calling for stiff sanctions against Israel because of its annexation of the Golan Heights.

Although Haig has signaled that he intends to prod the negotiations toward an early conclusion, he repeated that his main purpose at this point is to explore in detail the views of both sides and that he has no preconceived ideas about possible next steps.

He also underscored, as he did yesterday in Egypt, that although the United States would like "an early agreement," he is setting no deadlines and is not linking completion of an autonomy accord to Israel's scheduled withdrawal from the last third of the occupied Sinai Peninsula on April 25.

Both the United States and Israel are known to be seeking an agreement before the end of April, however, because of shared concern that if the situation drags on beyond Israel's scheduled pullback from the Sinai, the two sides will lose their incentive to pursue the autonomy talks seriously, and the Middle East peace process will lose momentum.

Egypt, while agreeing to cooperate in accelerated negotiations, has been in less of a hurry. Egyptian officials recently have made clear their doubts that a workable declaration of principles governing an autonomy plan can be hammered out in the next three months.

Complicating Haig's attempt to bridge the gap between Egypt and Israel is the fact that the secretary, who gave the autonomy talks a low priority during the first year of the Reagan administration, still has not decided on a formula for pushing the talks forward.

There has been speculation about the possible appointment of a high-level U.S. negotiator to take a hand in the talks or of Haig trying to mediate, either by shuttling between Jerusalem and Cairo or by arranging a conference with the two foreign ministers.

Washington Post correspondent William Claiborne contributed to this report.