As chairman of the National Republican Congressional Committee, Sessions steered Republicans to a landslide win in the 2010 elections. But as Republicans took over the House majority, he mulled a run against Rep. Kevin McCarthy (Calif.) to be Whip. Boehner ultimately dissuaded him.
"Everyone recognizes the great job Rep. Sessions has done at the NRCC. Should he want to pursue the Rules chairmanship, his talents would be well utilized there," said an aide with knowledge of the matter.
"As Chairman of the NRCC, all of my energy is focused on growing our Republican majority's historic gains last election. It is an honor to serve as vice chairman of the Rules Committee under Chairman Dreier — a stalwart defender of Republican principles — and I would consider it a privilege to build upon my 14 years of service on the committee by continuing his legacy of tireless leadership and consummate professionalism," Sessions said in a statement.
Sessions is also the conventional choice among his colleagues.
"Sessions seems to be the next person in line," Rep. Tim Scott (R-S.C.), a freshman Member of leadership who sits on the Rules Committee, said Tuesday. "I would be surprised if it's not him."
When asked a day before Dreier's announcement whether he would consider the chairmanship, Sessions said, "It's entirely up to the Speaker.
"I'm now in my 14th year being on the Rules Committee, and it's an exciting and wonderful place to be," he added.
Boehner spokesman Michael Steel on Tuesday declined to answer specifics about the chairmanship, as Dreier had not yet announced his retirement.
"Chairman Dreier is the chairman on the Rules Committee. If he ever chooses to make a change, we'll look at the options," he said.
The NRCC chairmanship is traditionally a two-term job. But Sessions may have higher ambitions than the Rules gavel. If he does decide on a run for a premier leadership post, sources speculate that Boehner could turn to Hastings to helm the panel.
Hastings is in his second term as the top Republican on the Natural Resources Committee. But the Washington lawmaker, who served on the Rules Committee from 1997 to 2007 and is one of Boehner's closest friends in the House, would be a natural choice to chair the Rules Committee.
While his current committee serves the interests of his home state exceptionally well, GOP rules limit Members to three terms as the top Republican on a panel, meaning that after the 113th Congress, he would be out in the cold. Although Boehner made an exception in allowing Dreier to keep his seat, there is no guarantee he would do the same for Hastings.
Hastings also was mum Tuesday on whether he is interested in another gavel.
"That's the Speaker's decision," he said. "I'm not even speculating on any of that stuff."
Correction: Feb. 29, 2011
An earlier version of this story incorrectly stated the number of years Rep. Doc Hastings served on the House Rules Committee. He served on the committee from 1997 to 2007.