The prospect that Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) is considering running for president again sent a message yesterday to the White House that key Republicans view President Reagan as vulnerable and unlikely to seek reelection.

Baker has indicated privately that he is leaning against running for a fourth Senate term and may run for president instead, in either 1984 or 1988. Several administration officials and advisers interpreted this as the latest signal from prospective candidates on Capitol Hill that Reagan should give an early indication of whether he will seek reelection.

"The president won't have the luxury of waiting for several months to decide with the sharks circling in the water," said one official. "He will have to give a very strong signal of his intentions in the next 45 to 60 days."

Another Reagan adviser said that the president "needs to make a signal to keep his political base."

One reason why prospective Republican candidates want such a signal is that they see the presidential nomination going almost by default to Vice President Bush if Reagan remains officially undecided through much of this year. A poll done by Penn and Schoen for David Garth in mid-December showed that Bush was far and away the preferred presidential candidate for Republicans if Reagan retired. The surfacing of what one White House official called "the Baker trial balloon" came after statements by two key GOP senators--Bob Dole of Kansas and Paul Laxalt of Nevada--jolted White House officials.

A month ago Dole complained that Reagan was insufficiently accessible. Last week Laxalt, the president's best friend in the Senate, publicly urged him to compromise on his economic policies.

Dole, however, has a reputation for outspokenness, and is an almost certain presidential candidate if Reagan doesn't run. Laxalt, whom some Republicans consider a prospective candidate under these circumstances, was excused by some White House officials on the grounds that he was carrying a policy message on behalf of his fellow senators and the White House staff.

But word that Baker was considering a presidential run had greater impact.

One administration official who discounted the probable success of a Baker candidacy observed that "Howard wouldn't be talking this way if he didn't suspect that Reagan might not decide to run."

Baker is vacationing in Florida and said through his press aide here, Tom Griscom, that he expects Reagan to seek reelection.

"But if Reagan doesn't run, Baker would look at it," Griscom said.

Dole said that he and Baker had lunch a couple of weeks ago and concluded that Reagan probably would run. Then, said Dole, Baker commented, "If he didn't run, there would probably be a mad scramble."

Dole, who ran briefly in 1980, did not deny that he would be a part of this scramble to follow Reagan.

"There are a number of us up here who feel we are destined to replace him," Dole said. "The voters may not have been informed yet."

Dole sent Baker a telegram yesterday saying, "Howard. Say It Isn't So."

The Kansan said Baker was "a terrific majority leader" and added he hoped he would stay in the Senate.

The Penn and Schoen poll taken for Garth found that Bush would be the choice of 36 percent of Republican voters if Reagan did not run. Baker was favored by 21 percent, Rep. Jack Kemp (R-N.Y.) by 7 percent, Dole by 6 percent and Sen. Jesse Helms (R-N.C.) by 2 percent with the rest undecided.

The results advertise what prospective GOP candidates already knew, which is that Bush has inherent advantages as vice president. These are likely to be enhanced by his impending European trip, where he will be a highly visible representative of the president.

Baker's willingness to be a candidate is likely to strain his relations with the White House, administration officials said yesterday. His relations already are strained with some of Reagan's core conservative supporters.

This week the conservative weekly Human Events, which Reagan reads, assailed Baker and Dole as "pragmatists" who, along with White House chief of staff James A. Baker III, are undermining the administration's conservative goals.

Some Reagan advisers fear that conservatives will begin shopping around for another candidate if the president is seen as unlikely to seek reelection. They want Reagan to step up his timetable for deciding on his candidacy.

However, one adviser warned that Reagan, already under heavy pressure to modify policies, would not be stampeded into a decision.

"He goes at his own pace, and he knows that things may look different in 90 days than they do now," he said. "He'll decide when he's ready, not when we are."