Rep. Edward R. Madigan of Illinois, the senior Republican on the House Agriculture Committee, has sent a letter to the White House expressing an interest in becoming the next agriculture secretary.

Madigan sent the letter Tuesday after he was encouraged by commodity and farm groups to put his name into consideration, Madigan press secretary Chris Kirby said yesterday.

Several others, usually in less direct ways, have put out the word that they would like to succeed Clayton Yeutter, who is resigning to become chairman of the Republican National Committee.

Former senator Rudy Boschwitz (R-Minn.), the only Senate incumbent defeated in the November elections, said he has been encouraged by conversations with White House officials about the position, and Sen. Robert W. Kasten Jr. (R-Wis.) issued a statement Tuesday calling on President Bush to nominate Boschwitz.

Others vying for the post are Deputy Agriculture Secretary Jack Parnell; Dean Kleckner, president of the American Farm Bureau Federation, the nation's largest farm organization, and Assistant Agriculture Secretary Jo Ann Smith. A Florida rancher, Smith was the first woman president of the National Cattlemen's Association, in 1985.

Another Republican House member, E. Thomas Coleman (Mo.), who also sits on the House Agriculture Committee, and two former GOP representatives, Bill Grant (Fla.) and Cooper Evans (Iowa), are said to be interested in the job. Evans, who recently left the White House as Bush's agriculture adviser, has the backing of the National Farmers Union.

Madigan has served in the House for 18 years. He was unopposed in November, but Illinois will lose two congressional seats after redistricting, and depending on how the map is redrawn, Madigan could be forced to run against House Minority Leader Robert H. Michel (R-Ill.) in 1992.

Republican officials speculated that Madigan's public job-seeking is a strong clue that Michel, who has hinted that he will not seek reelection, has changed his mind.

Kirby said Madigan, who lost a race for House minority whip in 1989 by two votes to Rep. Newt Gingrich (R-Ga.), is "happy in Congress," but "feels he could be more helpful to the president as secretary of agriculture."

A senior administration official said yesterday that the "list-compiling exercise" is at full throttle at the White House and that "any Republican member of Congress" would certainly be on the list if he asked to be. Bush had said after his 1988 election that to avoid potentially diminishing Republican strength in Congress he would not tap a current GOP lawmaker for a Cabinet post.

The official said Yeutter is not expected to formally leave the department until March 1 and "the choice is probably weeks off. The president is not exactly focusing on this this week."

Following the White House policy of naming all possible Republican candidates for a given job, the official named all of the above officials and several others. Bush has not been presented with a list and there "is no one, two, three right now," the official said.