First, though, 83-year-old Utah Republican Sen. Orrin Hatch must decide if he wants to run for an eighth term.
"I've had some conversations with Mitt Romney," McConnell told reporters. "Obviously, I'm an Orrin Hatch supporter. And Orrin has to decide what he wants to do. If he wants to run again, I'm for him."
Hatch told CNN on Friday that he speaks to Romney regularly -- but deflected questions about Romney, the former Massachusetts governor who is Mormon and owns a home in Utah, replacing him, saying it is "early to talk about this stuff."
"I've made the decision that I'm going to run, but things change," Hatch said.
Speculation about a Romney Senate bid has swirled since Hatch told the National Journal
last week that he has "expressed interest" to Romney in having him seek his seat, and could step aside "if I could get a really outstanding person to run for my position."
Hatch's communications director, Matt Whitlock, sent a statement later Friday from Hatch in which the Utah senator acknowledged that his "musing aloud" about his own future has "snowballed into a frenzy of premature speculation."
"While I have taken steps to run, I have yet to make a final decision," Hatch said in the statement. "While it's no secret that I hold Mitt Romney in extraordinarily high esteem, my musing aloud on the subject has apparently snowballed into a frenzy of premature speculation. While this sort of overhyped intrigue is great for selling papers, it simply doesn't reflect the reality of the situation, especially this soon after the last election. I remain focused on my work in the Senate and will make any political decisions in due course."
It has all left Utah Republicans unclear whether Hatch is serious about seeking re-election.
Talk about Romney, meanwhile, is viewed as much more hypothetical -- particularly because Romney has always been hesitant to close doors. A long-time adviser to Romney told CNN that "it's just a hypothetical exercise" fueled by Utah Republicans' desire for Romney to run unless Hatch decides against seeking re-election.
Romney's talks with then President-elect Donald Trump about the position of secretary of state suggested Romney is willing to consider a return to politics. A Senate seat would give Romney -- though just one of 100 members -- a platform to counter Trump, as well, much as he did during the 2016 campaign.
Currently, though, Romney is on a charity trip in Indonesia.
His son Josh Romney is also seen as a potential candidate for office in Utah.
Utah Republican Party Chairman James Evans downplayed a potential Romney bid, casting it as speculative at this point.
He said that after Hatch's comments to the National Journal, "people started talking. Of course they're going to approach Mitt Romney and say, 'Hey, would you run, what do you think?'"
"I'm sure his response would be, 'I would certainly consider it' or 'I'd think about it,' or something like that. And I think that's what this is all about," Evans said.
He added that "all of this has kind of thrown everyone."
"It's just hard to read whether Sen. Hatch is going to run again or not. It's just hard to figure that out," Evans said. "I just think he hasn't, in his mind, gotten to that place yet. And I think he has time. He doesn't have to give an answer today."