Secretary of State Edmund S. Muskie, in an appearance in Memphis last night, said that he has no intention of quitting the Carter administration and will stay in his post "as long as the president wants me to."

Muskie denied published reports that he is disenchanted with the policymaking process within the administration, saying, "I'm as enthusiastic about my job now as I was when I first accepted it. . . ."

In an interview yesterday with a Milwaukee television station, President Carter also denied the reports that Muskie did not plan to serve in a second Carter administration.

"That's a false report," Carter said. "I talked to Secretary Muskie last night. I won't use the exact language, but he said it was absolutely false. He enjoys his job. He and I have a very fine relationship. . . . He likes his job, he's pleased with what he's doing, and my hope is that he'll continue there."

Muskie's and Carter's remarks came in the wake of reports published in The Washington Star and The New York Times about the secretary's alleged unhappiness with his role in the administration and his competition with Carter's national security affairs adviser, Zbigniew Brzezinski.

The Star reported that Muskie expects to leave, and The Times said he would stay only if major changes are made in the management of foreign policy.

State Department sources said that following the appearance of the Star article on Sunday, Muskie had talked with the president and the two tentatively had made plans to squelch rumors of a rift.

State Department spokesman John Trattner, answering questions at his regular daily press briefing yesterday, said Muskie publicly has made clear several times since he became secretary in May that he has "no personal animosity" toward Brzezinski but that he has reservations about the way in which foreign policy decisions are made and carried out.

The spokesman added that if Carter wins a second term, Muskie can be expected to recommend changes in the way things are done.

Muskie's belief that the National Security Council staff directed by Brzezinski has too big a role in formulating and directing policy has caused differences to surface in a highly publicized way on at least two occasions.

In August, Muskie complained to reporters that he had not been consulted or informed of a decision by the president to change U.S. policy on targeting nuclear weapons. Last week, sources within the NSC staff leaked to reporters information that the decision to send radar command planes to Saudi Arabia represented a "victory" for Brzezinski over Muskie, whom they described as originally opposing the idea.

But, while these rivalries between State and the NSC staff are well known within the diplomatic community. State Department sources close to Muskie said yesterday they have seen no sign that he has become discouraged to the point where he plans to quit. If anything, the sources insisted, Muskie has indicated that he feels increasingly more comfortable in the job and eager to fight for the role of the president's top authority in the foreign policy field if there is a second Carter administration.