Both Senate President Michael Waddoups and House Speaker Becky Lockhart said Wednesday that they have been encouraged privately to run against Gov. Gary Herbert.
Neither is willing to rule out the Republican intraparty challenge, but they aren't throwing their hats into the ring, either.
"It's amazing how many people are dissatisfied and want somebody to run against him," Waddoups said. "I'm not planning on running at this point. â¦ There would have to be a groundswell out there and I don't envision that."
Waddoups has said previously that he won't seek re-election to the Legislature, where he has served for nearly 25 years. He is selling his business and said he and his wife are interested in serving a mission for The Church of Jesus Christ of Latter-day Saints.
Lockhart said she has been approached and is not closing the door to the possibility of running for governor, but said her focus has been on redistricting and is now preparing for the legislative session.
"It's very flattering that there are people out there who think I could run for governor or should run for governor," she said. "I would have to make that kind of decision before the session started if it was something I was going to do."
In the meantime, David Kirkham, a co-founder of the tea party movement in Utah, said he has been urged to run for governor and for U.S. Senate, and he is "seriously, seriously considering both options," but hasn't made up his mind which office, if any, he will pursue.