House Republican leaders are quietly encouraging Rep. Jeb Hensarling (Texas) to run to succeed Conference Chairman Mike Pence should the Indiana lawmaker choose to step down from his position to run for higher office, GOP sources said.

Pence, who is rumored to be eyeing a presidential or gubernatorial bid, has not declared he will step aside from his post and Hensarling has not publicly expressed interest in replacing him, but Republican sources familiar with discussions say Hensarling’s conservative credentials as a former chairman of the Republican Study Committee, close relationships with leaders and ability to raise millions of dollars for the National Republican Congressional Committee make him a prime candidate for the chairmanship.

“It’s no surprise that some in Congress are rallying around Hensarling. He’s a rising star in the Republican Party that would be absolutely vital to have at the leadership table,” said one House GOP aide with knowledge of the discussions. “He’s a beloved conservative who has never once checked his principles at the door.”

Sources familiar with the discussions between Hensarling and leadership say he is interested in the post but will not declare his intentions until after Pence decides whether to continue to serve as chairman.

Matt Lloyd, a spokesman for Pence, would not comment on the Indiana Republican’s intentions, saying in an e-mail that Pence is focused on Tuesday’s elections.

Hensarling’s spokesman also declined to comment.

The friendship between Hensarling and Pence is well-known within Republican circles. Hensarling put off a run for the Conference chairmanship in 2008 after Pence announced his intention to run at the behest of Minority Leader John Boehner (Ohio).

GOP aides and observers speculated at the time that Hensarling’s then-adversarial relationship with Boehner had caused the Ohio Republican to pull Pence into the leadership circle in order to protect his right flank.

Hensarling and Boehner have since mended their relationship.

Over the past two years, Boehner has appointed Hensarling to outside commissions such as the Troubled Asset Relief Program oversight panel and the National Commission on Fiscal Responsibility and Reform.

As a member of the Financial Services and Budget committees, Hensarling has become one of leadership’s go-to Members on matters of spending and financial reform.

Michael Steel, a spokesman for Boehner, declined to comment on the possibility of a Hensarling chairmanship.

“Our entire team is focused on Nov. 2,” Steel said in an e-mail.