Republican Conference Chairman Jeb Hensarling is a lock to lead the Financial Services Committee next year.
Though aides said that Hastings may have the right demeanor for the position - he is a previous Ethics chairman - they note that Sessions has proved himself at the NRCC, so leaders want to find a place for him.
If Hastings does indeed move to Rules, the Natural Resources gavel could be returned to former Chairman Don Young (Alaska) or the Steering Committee could tap new blood in Rep. Rob Bishop (Utah). Both declined to comment.
Ethics Chairman Jo Bonner (Ala.) said in an interview that he will not return to the helm of that panel. McCaul is the next in seniority on the committee, but Boehner could tap anyone for the thankless job, or at least anyone who is willing to take it.
Though House Administration Chairman Dan Lungren (Calif.) is not term-limited, he is in significant re-election trouble, making him the only sitting chairman who is in a tossup race.
Physician Ami Bera (D) is mounting his second challenge to Lungren in as many election cycles in a redrawn Sacramento-area district that is friendlier to Democrats than it was in 2010.
Rep. Gregg Harper (Miss.) is next in line, but he is running for Republican Conference secretary. It remains unclear who else the Speaker would consider for the committee that has oversight of campus operations.