Senate Minority Leader Howard Baker (R-Tenn.) yesterday formed a committee to explore his prospects for the 1980 Republican presidential nomination.

The committee, Baker announced, will raise money to finance his travel during the next five months while he tests the political waters. "It does not constitute an announcement [of candidacy]," he said. "But it does constitute an obvious interest."

Baker, who spent most of last fall either in the Senate or campaigning for reelection in Tennessee while other Republican presidential hopefuls were flying about the country, plans to begin his first series of trips next week.

He has scheduled stops in New Hampshire, Massachusetts, Ohio, New York, New Jersey, Tennessee, and Springfield, Ill., where he plans to lay a wreath on Abraham Lincoln's grave on Feb. 12, Lincoln's birthday.

Baker's announcement represents a marked stepping up of his presidential timetable at a time when the Republican presidential race is becoming increasingly crowded.

As recently as two weeks ago, his aides said he did not intend to form an explanatory committee until the end of February, and that he would not make a final decision on his candidacy until late summer. Now, aides said, he will make a decision about July 4.

Baker would like to have the strategic arms limitation treaty (SALT) and much of the year's legislative agenda behind him before he begins campaigning full time, his press secretary, Ron McMahan, said. But since the treaty's completion date has been delayed, Baker's decision most likely will be made regardless of the timing of a SALT vote.

Baker in recent months also has decided to keep his title as Senate minority leader should he decide to run for the presidency, while letting Minority Whip Ted Stevens (R-Alaska) take over the day-to-day duties of the post.

Baker aides say his early strategy is to use his post as minority leader and the recognition he gained six years ago on the Senate Watergate Committee to become the choice of middle-of-the-road Republicans.

It's based on the assumption that former California governor Ronald Reagan, whom Baker regards as the current frontrunner for the nomination, eventually will fall by the wayside, and the party will turn to a younger man. Baker is 53; Reagan is 67.

Baker is the third Republican hopeful to form an exploratory committee. Sen. Lowell Weicker (R-Conn.) and George Bush, a former congressman and ambassador, formed committees earlier. Two other Republicans -- former Texas governor John Connally and Rep. Philip Crane (R-Ill.) -- have formally announced their candidacies.

Among other things, the committees permit candidates to raise money that can be used for qualifying for federal matching funds. A presidential candidate who raises at least $5,000 in each of 20 states in contributions of $250 or less qualifies for public funding.

Baker, whose father and stepmother both served in Congress, was first elected to the Senate in 1966.