Amid rising speculation that she will call it a career, Sen. Muriel B. Humphrey (D-Minn.) has set tomorrow for an announcement on her possible candidacy for the balance of the term of her late husband, Sen. Hubert H. Humphrey (D-Minn.)

Humphrey is to announce her plans at a dinner in St. Paul, where Democratic notables are to pay tribute to the late senator.

Informed sources said they doubted she would exploit the occasion to announce her candidacy, so the speculation has grown that she will retire at the end of this year.

Her office, however, yesterday refused to comment on the speculation, and said she would say nothing on the subject until she speaks at the dinner, expected to draw some 5,000 of the Democratic Farmer-Labor Party faithful.

Her withdrawal would almost certainly give the party endorsement for the remaining four years of the Humphrey term to Rep. Donald M. Fraser (D-Minn.).

When Humphrey was appointed to her husband's seat last January, she was expected to serve only until the November election. But, to the surprise of other political figures in the state, she said she would reserve judgement on whether to run for the balance of the term. Polls in the state have shown her to be a strong candidate, if she ran.

But Fraser, 54, an eight-term House member from Minneapolis and champion of liberal causes, did not halt his own pursuit of the nomination. With Humphrey making no move to contest him, Fraser claims to have won endorsements already from 48 percent of the delegates to next June's state convention. Support of 60 percent of the delegates would give him the party endorsement.

Fraser was helped earlier in the week when State Sen. Nick Coleman (D), who had been poised to run for the nomination if Humphrey did not, announced that he was taking himself out of consideration.

However, Bob Short, a Minneapolis businessman who once owned the Washington Senators, has announced that he will run in the September primary if Humphrey is not a candidate. Short can run in the primary even if he does not seek the party endorsement.

The Republican side of the picture was also clarified this week when Rep. Thomas M. Hagedorn (R-Minn.) said he was "98 percent certain" to run for reelection, rather than seek the Humphrey seat. There was speculation that Rep. Bill Frenzel (R-Minn.) has also reached a similar decision.

Speculation among Minnesota Republican has turned to ex-Lt. Gov. Jim Goetz and to David Durenberger, a Minneapolis lawyer, as possible Senate candidates. Durenberger is now opposing Rep. Albert H. Quie (R-Minn.) for the endoresement for governor, but Quie is a heavy favorite to win that nomination and approve Gov. Rudy Perpich (D).

In the state's offer Senate race, also up this year, Sen. Wendell Anderson (D-Minn.) is expected to face Republican National Committeeman Rudy Boschwitz.