McConnell faces a potential challenger from the right going into his reelection cycle, as Tea Party groups in Kentucky are unhappy with what they see as his failure to adequately oppose President Obama's agenda.
Though Massie has been urged to run, he has said multiple times he's not interested.
"I haven't spent any of my mental cycles working on that problem at all," he told The Hill.
However, Massie was not as explicit when asked whether he'd be willing to back another primary challenger to McConnell.
"That's a complete hypothetical at this point, because I have a good ... I have my finger on the pulse in Kentucky and I haven't seen a credible candidate jump up," he said. "So to answer that question is a complete hypothetical, and I can't imagine a candidate who's going to get more than 40 percent of the vote in a primary, so it's not a good exercise to undertake."
Thus far, local businessman Matt Bevin has emerged as a potential Tea Party challenger to McConnell, and according to local news station WFPL, Bevin has recently been reaching out to Tea Party groups in central Kentucky.
Massie said that people in the state had contacted him seeking his support for a run, though he wouldn't offer names. He wouldn't comment on whether he had spoken with Bevin.
"You know, I've talked a few people off the ledge, I think," he said.
Launching a primary challenge against McConnell would be a decidedly uphill battle. Massie said that to those who have contacted him about a run, he's laid out the facts of a race against one of the most deep-pocketed, well-known politicians in the nation.
"I wouldn't name any of the folks. Suffice it to say, there are people who want to talk to me about this, and my advice to them is your floor in this primary is about 20 percent for a credible candidate, and then your ceiling, if you spend two years of your life, spend millions of dollars, it's gonna be 40 to 45 percent," he said.
"If you're frustrated, focus your frustration somewhere else, is my advice," he added.
And he said that, if McConnell were to face a credible challenger who managed to take a large portion of the vote and spend millions on attacks, "it could change the dynamic of the general election race in a bad way for Republicans."
Looking toward 2016, Massie offered unequivocal support for Sen. Rand Paul (R-Ky.), who shares a libertarian streak with the congressman.
And he left the door open to pursuing Paul's seat if the senator does run for president, as is likely. Asked repeatedly whether he's interested in the seat, Massie said he wouldn't comment because he found a focus on future political gains "hypocritical."
"We could start working on [the government's spending problem now,] but the problem is, everyone is focused on 2014 and keeping the majority here so it would be hypocritical of me to say that people are are too focused on 2014 and then comment on a race in 2016 for myself," he said.
However, Massie said that keeping the majority in 2014 is important, because it would be "almost like a post-apocalyptic scenario if we lose the House and President Obama has complete control of all the branches of government."