Rep. Jason Chaffetz (R-Utah), who announced this week he won’t run for office in 2018, has not said publicly when he plans to resign. (Kim Raff/For The Washington Post)

A rift between conservative and mainstream Republicans is already emerging about who should replace Rep. Jason Chaffetz (R-Utah) as chairman of the powerful House Oversight and Government Reform Committee when he departs Capitol Hill.

Chaffetz, who announced this week he won’t run for office in 2018, has not said publicly when he plans to resign.

Republicans believe that he will surrender the gavel in the coming weeks, leading supporters of possible replacements to begin maneuvering for the helm of the House’s chief investigatory panel.

A bloc of conservatives is advocating for Rep. Jim Jordan (R-Ohio) to receive the chairmanship. Jordan is an outspoken member of the House Freedom Caucus who has clashed repeatedly with GOP leaders.

Mainstream Republicans are eyeing Rep. Michael R. Turner (R-Ohio), a more moderate voice who has served on the Oversight Committee but is not currently a member.

(Jenny Starrs/The Washington Post)

Both are thought to be interested in the position, Republican sources said. Jordan and Turner competed for the gavel 2½ years ago, but the House GOP Steering Committee, mostly made up of House leaders and their allies, instead backed Chaffetz for the post.

Colleagues see a wild card in Rep. Trey Gowdy (R-S.C.), the former federal prosecutor and chairman of the House Select Committee on Benghazi. Trusted by both leadership and conservatives, Gowdy has the inside track for Chaffetz’s position, according to two senior Republican aides. But, the aides said, it is unclear whether Gowdy wants such a controversial post under President Trump.

The race is expected to move quickly because Chaffetz has indicated he’s already looking for private-sector employment and might soon resign, prompting leadership to believe that he needs to transition out of the powerful committee post for reasons of appearance. There’s speculation the Utah Republican might leave Congress as early as the end of May or in June.

“I might depart early,” Chaffetz told Politico this week. “It’s not tomorrow, it’s not next week. If it is, it’s going to be in the months to come.”

The early jockeying underscores the desirability of the high-profile post. But the job is also considered less palatable under a Republican administration. Chaffetz was known for his aggressive investigations of the Obama administration but has not sunk his teeth into possible conflicts of interest surrounding President Trump and his sprawling business empire.

Requests for comment from Chaffetz, Jordan and Turner were not returned Friday afternoon. Gowdy’s spokeswoman declined to comment on the record.

A spokeswoman for Speaker Paul D. Ryan (R-Wis.), AshLee Strong, emailed Friday that Ryan has “full confidence in Chairman Chaffetz.”

She pointed to a recent tweet from Ryan saying that he was “thankful” to have served with Chaffetz, a “great defender of liberty and limited government.”

The decision about who should replace Chaffetz will be made by the House Republican Steering Committee.

Jordan would appear to be an underdog, based on the leaning of the steering panel, especially since, in the time since he lost out to Chaffetz, he has become even more of an antagonist toward leadership. However, there are concerns about the fallout if he is again passed over for the gavel.

The chain of seniority on Oversight — which would normally serve as a possible line of succession — does not help in this case.

Behind Chaffetz is Rep. John J. Duncan Jr. (R-Tenn.), who is understood to be waiting to claim the gavel at the House Transportation and Infrastructure Committee once Rep. Bill Shuster’s (R-Pa.) term as chairman ends.

After Duncan is Rep. Darrell Issa (R-Calif.), who served as Oversight chairman until Chaffetz succeeded him.

Jordan ranks fourth after Issa, with Gowdy several positions down the list.

One senior Republican aide predicted major fallout for Republican leaders if they make Turner chairman. Freedom Caucus members are not likely to welcome the notion that Jordan was passed over for a moderate Republican who is not even a member of the committee.

Gowdy could be a possible compromise choice, though a source close to him seemed to play down the idea, noting he has never sought a chairmanship (despite being chosen as head of the Benghazi panel) and is already on four committees.