Is there a gleam in Jimmy Carter's eye?

The Jimmy Carter who walked into a meeting with a large group of reporters the other morning was the amiable Jimmy Carter that everyone found so irresistible in the days before he became president.

For those visiting the White House the Carter warmth stayed on. No one could be more hospitable to guests than the President and First Lady Rosalynn.

But with the responsibilities of the Oval Office came a tight-lipped, often steely-eyed Carter in his day-to-day operation. Everybody's-friend Carter became no-nonsense Carter. Even that wide, beautiful smile faded. And with the hostage crisis, Mr. Carter turned very serious in his demeanor.

And understandably so. With Iran gouging him on the one side and Teddy Kennedy's challenge pricking him on the other Mr. Carter found little to light up his life, and his face, in that last year as President.

And his account of this travail in his newly published book, ''Keeping Faith, '' will doubtless (a) cause many readers to sympathize with him and (b) reinforce their views that no one with half an ounce of sense would actually want to seek these awesome presidential burdens.

Jimmy Carter wrote every word of these memoirs. That's worth mentioning. If the prose may be a little less than sparkling, it is comforting to know that this is Carter talking, not some ghost writer. Other former presidents of recent vintage have leaned heavily on skilled writers to hone the final product. One recalls how John F. Kennedy's ''Profiles in Courage,'' which helped catapult him to national attention and toward the presidency, was so heavily infused with outside assistance. And Ray Price's strong editing role is quite apparent in Richard Nixon's books, particularly his latest on ''Leaders.''

But the reporters were not there that morning to hear about the new Carter book - although Carter's main reason for being there was to boost its sales. They were there, many said as they waited for Carter's arrival, to see what he was ''up to.'' Was Carter plotting a reemergence on the political scene? Indeed, could this relatively young ex-President be making some preliminary moves toward another run for the presidency?

Carter, after shaking hands all around, wasted no time in addressing the ''running-again'' question. ''I haven't given it any thought,'' he said, his voice dropping to the place where listeners at outer tables were having to strain to hear.

This was certainly no strong Carter disclaimer of such intentions. Thus, the impression he left, as he turned to other subjects, was that there just might be circumstances under which his presidential aspirations might once again be rekindled. Perhaps not likely. But there seemed to be a possibility that this could happen.

In this vein, some reporters found it relevant that Carter opened up some space between himself and his vice-president, Walter Mondale, in his comments. He said he didn't agree with Mondale's apparent position in favor of the US moving toward protectionism in trading with Japan.

Q: How do you feel about Mondale's proposal that the US ''get tough'' with Japan? A: I don't agree with him. Q: Is it good politics or bad? A: It is not good for our country. I don't know about the politics. . . . We can't blame all our economic problems on world trade. We are already approaching a trade war. . . . I'm not condemning Mondale. We just don't agree on the Japanese question.

Carter then made it clear that his ''preference'' among potential presidential candidates is Mondale. ''He wants to run his own campaign to separate himself from me,'' Carter added here. ''I think it is advisable for him to run his own campaign. I don't want him to inherit my problems.''

After the breakfast some reporters were asking: Was Carter separating himself from Mondale on this major trade issue as a help to the Mondale candidacy? Or was Carter a little miffed at Mondale's persistent efforts to show that he was his own man? Indeed, was Carter seeing in these efforts an implied criticism of the Carter leadership? One newsman put it this way:

''Why did Carter jump on Mondale so hard on this issue? He could have said he was sure that Mondale was simply in the process of firming up his thoughts on this and other issues - or something along that line. And let it go at that. But Carter went on to say that he thought Mondale's motivations were political - in order to pick up labor's endorsement. That's pretty tough talk when you're speaking about an old friend and cohort.''

Since the breakfast Mr. Carter has continued to thump his antiprotectionist theme. Most recently, he has joined with Gerald Ford in a statement, published in the New York Times, which urges governments to establish ''good public policy'' by ''collectively resisting the protectionist pressures of self-interest groups.''

Could it be - some reporters are asking - that Carter is laying the groundwork for another run at the presidency in the event that the current crop of visible candidates turns out to be unacceptable to the Democratic voters?

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