"We put out name out there," Westmoreland told The Daily Caller on Thursday. "People know we are interested in it, so we’ll see what happens."
Earlier on Thursday, US House Majority Leader Kevin McCarthy said he would not run for the speaker position in the lower chamber of Congress.
The new speaker will take over US Congressman John Boehner, who suddenly announced his resignation from the leadership role on September 25.
On Monday, Boehner said House leadership elections would take place on October 29. Prior to the final vote, the members of the House Republican Conference were expected to elect a nominee for the speaker’s position, but McCarthy’s decision has postponed the process.