Rep. Thomas M. Hagedorn (R-Minn.) is expected to annouce Monday that he's interested in running next year for the U.S. Senate seat held by Democrat Wendell Anderson.

This challenge would also place Hagedorn, a conservative second-term, in competition with fellow Republican Rudy Boschwitz, a moderate member of the Republican National Committee, who has been actively campaigning for the senatorial nomination.

However, sources close to Hagdorn, a 34-year-old farmer from Truman Minn., said his real strategy is to position himself for the vacancy that would occur if Sen. Hubert Humphrey leave office for health reasons before his term expires in 1982.

This reflects a shift in the public's attitude on the political implications of Humphrey's illness. Up to now, people in both parties here have avoided talking publicly about the possibility that Humphrey, 66, whose cancer is inoperable, might not be able to finish his term.

But Saturday, in a development related to Hagedorn's ambitions, Rep. Donald M. Fraser, (D-Minn.) said: "Sen. Humphrey has advised me that it is appropriate for me to discuss publicly my interest in succeeding him in the U.S. Senate."

Fraser made this disclosure as he announced he had give up the idea of seeking party support for a 1978 contest against incumbent Anderson, a former governor who filled the Senate seat vacated a year ago by Vice President Mondale. Anderson recently got Humphrey's backing for a full-term bid, but this arranging his own appointment has cost him popular support.

These developments opened the possibility of a clear-cut contest between the conservative Hagedorn and Fraser, a liberal who has been in Congress since 1963, if Humphrey's seat becomes vacant.

Present state law empowers the governor to fill Senate vacanies by appointment, but the legislature is expected to pass, and Democratic Gov. Rudy Perpich is expected to sign early next year, a law providing for a special election when such a vacancy occurs.

Fraser said here Saturday he had discussed the Minnesota political situation twice in the past week with Humphrey, adding:

"He, himself, has spoken of the possibility that he may have to resign if the burdens of public office become too great. We hope and pray that this will not happen and that he will be successful in his courageous and inspiring battle to regain his health."

Fraser's decision not to challenge Anderson was hailed at a meeting of his Democratic Farmer-Labor Party's State Central Committee as a move to avoid "ripping up the party." John Connolly, of St. Paul, a liberal activist, has announced he would run against Anderson but he is not expected to make headway in getting the nomination.