President Reagan met with U.N. Ambassador Jeane J. Kirkpatrick yesterday and kept open the possibility that she will play a major role in his second term. Kirkpatrick said she plans to meet Reagan again after his Jan. 20 inauguration.

Administration sources and conservatives close to Kirkpatrick said she might become counselor to the president, replacing Edwin Meese III, the attorney-general nominee. Others said Reagan may create a temporary "trouble-shooting" job, presumably dealing with foreign affairs.

"We talked a bit about the future and agreed to talk again sometime after the inauguration. And that's all I'm going to have to say," Kirkpatrick told reporters after the half-hour session in the Oval Office.

White House spokesman Larry Speakes said after the meeting that Reagan approved Kirkpatrick's statement in advance and that the president "doesn't want to say any more."

Kirkpatrick, a favorite of conservatives, has announced plans to leave the United Nations and return to her Georgetown University professorship. She has made clear that she would remain in the administration only if offered a major position, and conservatives have urged Reagan to appoint her to an important post.

Reagan said recently that he had no position "that would be worthy of her." But several officials within and outside the administration said they interpreted the outcome of yesterday's meeting as a sign that the president is still searching for one.

"The president values her services," an informed official said. "He really wants to keep her on. He's just got to find a way to keep her on."

This official said Reagan and Kirkpatrick appear to have "bought some time" with yesterday's session. "She's not going to be running around anymore talking about her future," the official said.

No aides or other officials attended the meeting.

A Republican with close ties to the administration said conservatives urged Kirkpatrick before the meeting to request the job of White House counselor. But Kirkpatrick replied that she would not ask Reagan for a position, the source said.

Kirkpatrick told reporters that she discussed with Reagan yesterday how the United States is faring at the United Nations. "He agrees we're doing a lot better than we used to but there's still quite a ways to go," she said.

Kirkpatrick is expected to remain at the United Nations until Reagan names a successor. Administration officials said they believe that she will stay at least until February or March.

By that time, or at least by the time of her next meeting with Reagan, the president may have a better idea about what positions are available, officials said. Meese probably will have been confirmed by the Senate at that time, they added.

Administration officials had said they believed that Kirkpatrick was interested in such posts as secretary of state, Central Intelligence Agency director or national security affairs adviser after last month's election. But, after Election Day, Reagan asked all of the incumbents to remain.

A conservative Democrat, Kirkpatrick came to Reagan's attention through an article she wrote for Commentary magazine in which she accused the Carter administration of preferring hostile leftist governments rather than authoritarian, rightist regimes that were U.S. allies.

On domestic policy, Kirkpatrick has described herself as a "liberal, welfare-state Democrat," leading some White House staff members to question whether she would fit in as a presidential counselor.

A leading administration conservative said yesterday:

"It may be true that Jeane has some differences with the president on domestic policy, but so do they," referring to chief of staff James A. Baker III and other so-called "pragmatists" at the White House.