Rep. Liz Cheney Elizabeth (Liz) Lynn CheneyOVERNIGHT ENERGY: Cheney asks DOJ to probe environmental groups | Kudlow: 'No sector worse hurt than energy' during pandemic | Trump pledges 'no politics' in Pebble Mine review Cheney asks DOJ to probe environmental groups Press: The big no-show at the RNC MORE (R-Wyo.) brushed aside questions about a possible Senate bid on Wednesday, saying she had no announcements to make.

Cheney, the House Republican Conference Chairwoman, is seen as a favorite to succeed the retiring Sen. Mike Enzi Michael (Mike) Bradley EnziChamber of Commerce endorses McSally for reelection Cynthia Lummis wins GOP Senate primary in Wyoming The Hill's Convention Report: Democrats gear up for Day Two of convention MORE (R-Wyo.) if she decides to run for the Senate. But she’s also the third-ranking House Republican leader, meaning she could also have a bright future in the lower chamber.

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“I don't have any announcements to make about that other than to say how privileged I am to call Mike Enzi friend,” Cheney, who challenged the retiring senator in a primary in 2014 before withdrawing from the race.

“What a tremendous mentor he has been — he's going to be in the Senate for another 18 months,” she told reporters at a press conference Wednesday.

“I look forward to continuing doing work for people back in Wyoming, with [Sen.] John [Barrasso (R-Wyo.)] and Mike [Enzi] with our whole delegation and working here with our leader, Kevin McCarthy Kevin Owen McCarthyMcCarthy threatens motion to oust Pelosi if she moves forward with impeachment Kate Schroder in Ohio among Democratic challengers squelching GOP hopes for the House McCarthy's Democratic challenger to launch first TV ad highlighting Air Force service as single mother MORE [R-Calif.] and our Whip Steve Scalise Stephen (Steve) Joseph ScaliseHouse GOP slated to unveil agenda ahead of election House panel details 'serious' concerns around Florida, Georgia, Texas, Wisconsin elections Scalise hit with ethics complaint over doctored Barkan video MORE [R-La.] on the issues we've been talking about the matter so much the American people,” she added.

One GOP lawmaker said the nomination is likely hers if she wants it, arguing she could stave off the field until she ultimately decides to make her decision.

“I mean, this doesn't happen very often, and remember she, went to run for it last time. She doesn't have to make a decision soon,” the lawmaker said. “I think she could hold the people at bay for a while.”

Cheney attended a fundraiser for Alabama Senate-hopeful Rep. Bradley Byrne Bradley Roberts ByrneBottom line Jerry Carl wins GOP Alabama runoff to replace Rep. Bradley Byrne Jeff Sessions loses comeback bid in Alabama runoff MORE (R) on Monday, which some took as a signal that she has her eyes set on the upper chamber.

“She and I are very close friends, so on a personal basis, I'd love to see her over in the Senate," Byrne said. “On the other hand, she's doing a terrific job for our conference here. She's providing leadership that we really need at this point in time now that we're in the minority. I think she provides an incredibly important role here.”

A recent rule passed by the Republican conference would require members of leadership to relinquish their role should they announce they are seeking higher office.

In response to a question on whether conference rules could be amended to allow her to remain in her position through the end of her term in the event of a Senate announcement, McCarthy said no decision had been made.