Leavitt said Monday he knows who Walker has chosen, "and Utahns will be well-served" by that person.

Walker has not said whether she will run for governor next year or not, although several years ago she told the Deseret Morning News that, if not for her age, she would seriously consider running in 2004 should Leavitt retire. Walker turns 73 on Nov. 15.

Picking a second-in-command running for governor in 2004 could pose some problems, if the person has opposing views of the governor. The lieutenant governor would also be needed in the state Capitol, helping run a short-term administration.

Other names being floated as possible choices for lieutenant governor include:

• Nolan Karras. A gubernatorial candidate, Karras is a former House speaker who was the governor's representative on the board of trustees for the Salt Lake Organizing Committee.

Karras is Walker's close friend from the days they were both legislative colleagues, and Karras is unflaggingly loyal to Walker and Leavitt.

But politicos say it does not help Karras' campaign — and might even hurt him — to run a campaign while playing second fiddle to a lame-duck governor.

Although, there is a precedence for a lieutenant governor rising to higher office, sources say the new lieutenant governor would have to resign any other elective office he or she now holds, thus cutting down on the likelihood a top GOP legislator looking to be House speaker or Senate president would want the short appointment.

• John Valentine: That would eliminate Valentine, R-Orem, the Senate majority whip, who fueled the speculation when he showed up at Leavitt's Tuesday press conference on the governor's confirmation as administrator of the Environmental Protection Agency.

"I will not be the next lieutenant governor," Valentine told the Deseret Morning News. "I want to be the next Senate president."

Valentine, a veteran of the House and Senate, said he has been hearing the rumor all day. But there is nothing to it, he said, although he added he is "reserving the right" to consider becoming the running mate to a Republican gubernatorial candidate next year. Valentine has been mentioned from time to time as a candidate for the U.S. House and is rumored to have larger political ambitions than the Legislature.