Rep. Trey Gowdy (R., S.C.) could become chairman of the House Oversight and Government Reform Committee following the June 30th departure of the current chairman, Rep. Jason Chaffetz (R., Utah).

Gowdy, who led the two year House Benghazi probe, has “near unanimous” support from the 36-member House Republican Steering Committee that determines chairmanships, the Washington Post reported Tuesday.

Gowdy has declined to comment on his interest, and a Gowdy spokeswoman told the Post that the congressman “is continuing to speak with members in the conference about the qualities they believe are most important for the next Chairman to possess.”

Several committee members said they were backing Gowdy, and that he was ready to take up the job. Rep. Tom Graves (R., Ga.), a Steering Committee member, said he plans to nominate Gowdy.