"If we don't focus on what we told the American people we're going to do over the next six months, we're not going to be in the majority," he said. "My focus is on the next six months."
He said Republicans must keep campaign promises to do welfare reform, make the tax cuts permanent, stop "the crazy spending" in order to win voters' support.
"As I've said before, there is no race right now," he said, but if there is one, "I'm definitely open to consider it."
Among those believed to be considering running for the top House job should Republicans win the House in November are House Majority Leader Kevin McCarthy of California.
Jordan said he had been urged to run by colleagues, but did not name them, though House Freedom Caucus Chair Mark Meadows suggested the notion to CNN.
Larry Sabato, director of the Center for Politics at the University of Virginia said while “Jordan certainly isn’t viewed as the likely next Speaker right now… unknown events, scandals, and the election results in the fall could shake up the field.”
Were Jordan to run and win, he'd be the second Ohioan to hold the number one position in the House: House Speaker John Boehner held the post from 2011 until 2015, when he stepped down in part because of frustration with conservatives such as Jordan. When Boehner served in Congress, his western Ohio district directly abutted Jordan's.
In an interview this week, Boehner dismissed the idea of conservatives such as Jordan winning the speakership, saying they'd fall far short of the 218 votes needed to win the position.
“They know they can’t win,” he said. “So I’m sure that’s not going to happen.”