With teasing but calculated hints, President Reagan and his senior advisers have been intentionally fueling speculation that he will seek a second term.

In a political speech, Reagan declared that he wants Vice President Bush on the ticket should he run.

In a tape-recorded message for long-time Reaganites, he talked about the unfinished work of his administration.

And White House chief of staff James A. Baker III compared Reagan last week to a Kentucky Derby horse in the starting gate, all set to run.

But in private moments with his staff and White House visitors, Reagan appears far more reserved and less engaged in the question of a second term than public hints suggest.

In these private encounters, Reagan remains studiously noncommittal about the reelection question, according to several people who have raised it with him.

Although his Democratic rivals have begun the 1984 campaign, increasing anxiety among Senate Republicans who will be on the same ticket, Reagan appears to those around him to be in no hurry to join the fray.

Whatever his decision, these associates say, Reagan seems inwardly secure about it and in no mood for discussion. He does not even want to joke about it privately, they added.

Last week, for example, Reagan hosted a dinner for 15 of 19 Republican senators up for reelection in 1984.

At one point, a participant said, Senate Foreign Relations Committee Chairman Charles H. Percy (R-Ill.) handed Reagan a business card and said in jest that it named Percy's campaign consultant--should Reagan decide to run again.

While the senators watched intently for a sign about his intentions, Reagan did nothing.

"He laughed, but he didn't indicate any feeling," recalled one senator present. "He didn't jump in and get wet."

Before Reagan's 1976 and 1980 presidential campaigns, his top advisers were confident, long before he officially told them, that he would run.

All of Reagan's senior staffers have been sending signals that he will be a candidate. The president aroused a group of longtime supporters, members of the political action committee Citizens for the Republic, with a pretaped message at their annual dinner May 5 in Los Angeles in which he declared: "We've come so far, we must not--we will not--give up now."

But in private meetings at the White House, Reagan often volunteers, without being asked, that he has not made up his mind, officials said.

This is because does not want to give private hints different from the public line, one official said.

Reagan has a stock answer for those in public and private who press him about reelection plans. He says it makes no sense to decide this early because either way it would hurt his presidency.

"If the answer would be one thing, I would become a lame duck," Reagan said recently.

"And if the answer was the other way, yes, then everything I tried to do would be viewed by the opposition as part of a political campaign and maybe we couldn't get as much bipartisan cooperation as we need.

"We're not playing any games or anything," he added. "I know that it has to be done, but I don't think this is the time to do it."

His political and policy strategists believe that Reagan must take a bipartisan approach to troublesome foreign policy problems and wait as long as possible to enter a more partisan environment.

Based on his 1980 experience, Reagan is known to think that the campaign season is too long. "He really does subscribe to the idea that the political season is too long, it can go stale," one official said. By waiting, the official added, Reagan thinks "the public will get tired of Democrats first."

The president's schedule hinges on his August vacation at his California ranch.

With expectations rising that Reagan plans to seek a second term, the vacation really is "when he decides if he shouldn't run," an informed official said.

If he is running, by late summer or at least early fall, Reagan will authorize formation of an "exploratory" reelection committee, the official said.

The president has been reluctant to do so earlier.

Reagan "doesn't see any value" in making a formal announcement too early, one official said. It will most certainly come after Labor Day and perhaps as late as mid-October, the official said.

"It will be very apparent by September," another official said. "Those cute little hints that are now coming every day will come every paragraph."