Conservatives are seeking to oust the most liberal member of the Senate Republican leadership Tuesday as part of a broader bid to strengthen their policy-making role within the GOP.

In party caucuses they are backing Sen. Thad Cochran (Miss.), who is popular in both moderate and conservative wings of the party, in his effort to replace Sen. John H. Chafee (R.I.) as chairman of the Senate Republican Conference, the third-ranking GOP leadership post.

Races for several lesser party posts also are becoming ideological in nature in what appears to be a concerted effort by conservatives to win and use party posts to advance their agenda both within the Senate and in dealings with the White House.

Although a friend and supporter of President Bush, Chafee has often angered conservatives by straying from the party line on sensitive issues of particular concern to conservatives, most recently voting to overturn Bush's veto of the 1990 Civil Rights Act. The veto was narrowly sustained.

Both Chafee and Cochran, now the Republican conference secretary, have indicated they are optimistic about their chances. The outcome is seen as uncertain.

Neither Minority Leader Robert J. Dole (Kan.) nor Minority Whip Alan K. Simpson (Wyo.) is being challenged, although conservatives explored the possibility of running a candidate against Simpson earlier in the year.

On the Democratic side, Senate Majority Leader George J. Mitchell (Maine) has no opposition, and Sen. Wendell H. Ford (Ky.), who made an unsuccessful last-minute bid two years ago for the post of whip, or assistant minority leader, is expected to get the job this time.

The post is now held by Sen. Alan Cranston (Calif.), who announced Thursday that he will relinquish the job and will not seek reelection to his Senate seat in 1992 because he has prostate cancer.

Cranston, one of five senators under investigation by the Senate ethics committee for their involvement with failed savings and loan executive Charles H. Keating Jr., faced probable defeat by Ford in the whip race as well as bleak prospects for reelection in California.

After Cranston withdrew, Sen. David Pryor (Ark.), now the third-ranking Democratic leader and a popular figure with many of the Senate's newer members, tested the waters for two days. But Pryor announced yesterday he would run again for his current post as secretary of the Democratic Conference and endorsed Ford.

Ford, chairman of the Senate Rules Committee, has been preparing to run for whip for two years and reportedly had at least 35 votes from among the 56 Democrats.

"When I started making phone calls, I found that Wendell had strong support from our colleagues. . . . I count myself as one of his supporters," Pryor said yesterday.

In the only other Democratic race, Sens. Charles S. Robb (Va.) and Richard Bryan (Nev.) are vying to become chairman of the Democratic Senatorial Campaign Committee. This job, which normally changes hands every two years, is filled by the majority leader, and Mitchell has not yet indicated whom he will pick.

With Cranston gone, selection of Bryan would give the West a post in the leadership, but regional balance, while often important, is not always a determining factor in leadership contests.

On the Republican side, part of the conservative push stems from the retirement of Sen. William L. Armstrong (Colo.), who headed the Republican Policy Committee and was the strongest conservative voice in the leadership.

But it also reflects a desire to push the Bush administration to the right on fiscal and social policy and to use the Senate Republican leadership as an instrument for achieving that end.

With the exception of Cochran, other top leaders, including Dole and Simpson, cannot be counted as true-blue conservatives on such litmus-test issues as opposition to tax increases under any circumstances. Nor can some of the contenders for vacant leadership posts this year, such as Sen. Pete V. Domenici (N.M.), who is running to succeed Armstrong as head of the policy committee.

Challenging Domenici is Sen. Don Nickles (Okla.), the outgoing chairman of the GOP senatorial campaign committee, whom many conservatives see as a rising star within their ranks.

Running to succeed Nickles as chairman of the campaign committee are Sens. Phil Gramm (Tex.) and Mitch McConnell (Ky.). McConnell won points from many Republicans for his ultimately successful effort to derail Democratic legislation to impose campaign spending limits, although Gramm is viewed as the more conservative of the two and an emerging conservative figure on the national scene.

Candidates for secretary of the Republican conference are Sens. Christopher S. Bond (Mo.) and Robert W. Kasten Jr. (Wis.), with Kasten probably lining up more with the conservative faction than Bond does on most issues.

In his bid for the No. 3 spot, Cochran has been playing down ideological implications and stressing the need for "new ideas and new energy" in the job that Chafee has held for the past six years. Among other things, Cochran is proposing task forces to develop alternatives to Democratic initiatives.