05/08/2012 04:00 pm ET Updated May 08, 2012

Mike Enzi: Liz Cheney 'Can Run For Anything She Wants'

WASHINGTON -- Liz Cheney's recent appearances across Wyoming have sparked rumors that the former State Department official and daughter of Vice President Dick Cheney might be considering a U.S. Senate run there. But the seat's current Republican occupant hasn't said he plans to retire.

"She can run for anything she wants to," said Sen. Mike Enzi (R-Wyo.) when HuffPost asked him about a 2014 Cheney run.

This past weekend, Cheney sidestepped a question on "Fox News Sunday" about whether she's planning a Senate bid, saying only, "I love Wyoming. Wyoming is my home."

Whether Wyoming sends her to Washington in January 2015 will have much to do with whether Republicans retake control of the Senate in the coming election. Republican control of the upper chamber would make Enzi the powerful chairman of the Health, Education, Labor and Pensions Committee.

"I had some difficulty when I came up for election last time because I'd been turned down twice for a Finance [Committee] position when I had the seniority for it," Enzi said. "And I'm an accountant; I want to work on taxes. But I'm now on the Finance Committee. And if we're in the majority, I'll be a chairman of the Health, Education, Labor and Pensions Committee, which I really enjoyed doing before."

Enzi won reelection by large margins in 2002 and 2008. Moreover, he said he's considering running again in 2014.

"Well, you know, it's a long time before that," he said. "But I think at the state convention, I made some kind of statement about some antiques I was saving for a fundraiser for my reelect."

Ryan Grim contributed reporting.