Rep. Paul Ryan of Wisconsin has so far rebuffed calls to run for the House's top position.
Spokeswoman Heather Swift says Zinke's decision will depend on what Ryan does.
Zinke says callers to his office have been urging him to run. He says other freshmen congressmen have been elected speaker but it has been a long time.
When Boehner announced his resignation last month, Zinke said he was looking for a new speaker who shows resolve against President Barack Obama and bureaucrats "who have hijacked the U.S. Constitution."