Yes I do, but that doesn't mean it's going to be easy or will happen. I would think one of the two winter leagues (NBA/NHL) is the more likely scenario, but I suppose MLS could be of interest. NFL and MLB are probably long-shots, especially NFL with nearby Cincinnati and Indianapolis already occupied.
Louisville has a few things in their favor, they've got a couple of Fortune 500 companies in town (KFC Yum Brands and Kindred Healthcare), another that drifts in and out of the list (Humana), and they've also got Papa Johns, a Ford motor plant, and UPS Airlines has their Worldport there. So there's corporate support in place. They also are a tourist destination, sort of a Nashville-light I guess (Kentucky Bourbon trail and the Derby are popular w/ out-of-towners). They would also have no competition in state except for NCAA, which could be a bit of a deterrent, but other markets like Raleigh and Columbus, and even Nashville have to compete with NCAA as well.
According to Google, Kentucky appears to have two Billionaires living in the state. One is B. Wayne Hughes, founder of Public Storage and an investor in Horse Racing and the other is his own daughter. Mr. Hughes is in his 80's and his daughter is in her late 50's. Are either interested in being an owner for a sports team? Nothing I've seen suggests so and I would doubt it at this time, especially at this stage in their lives. So this would mean an out-of-stater would likely have to get involved.
Naturally, the NBA would be the perfect fit since the state is hoops-crazy. The market would be similar to other markets like Memphis, Orlando, OKC, Sacramento, Utah, Portland, and San Antonio in that they would be NBA-only or only have MLS to deal with on a major-league level. However, the NBA and small-markets I think are kind of at an impasse right now. The franchise in these markets tend to be bottom-feeder to the big boys and w/ the NBA being a superstar-driven league, that's just going to make recruiting and keeping star players all the more harder, we will see what happens w/ Giannis in Milwaukee next summer. Louisville might be interesting to some U of K stars to play there, but then again a lot of that programs top talent comes from other states.
What I do think the city could potentially support, would be yes, the NHL, especially if they had a Vinik/Dundon or even a Nashville-type of owner. It's a college market, similar to Raleigh, Nashville, and Columbus. It's a growing market, not quite as rapidly as others but still growing. It's 46th largest metro puts it in the "realm" with Buffalo, New Orleans, Salt Lake City, and Memphis, so it's on the smaller scale but it's "do-able". It's TV market is also on the smaller scale but still "do-able". It would be the only other NHL-only US market besides Raleigh, and unlike Raleigh they would have the state of Kentucky to themselves, and possibly even market to Indiana, which has no NHL franchise.
Now comes the real question. U of L has their mens/womens hoops and volleyball teams, and other university events, hosted at KFC Yum Center. Are they willing to share? I would doubt it. The building itself seems perfect for the NBA, not really sure for NHL but it's in a good location, it's somewhat new, and appears to have adequate number of suites. It's just again, U of L occupies the building heavily during the NBA/NHL seasons.
So yes, of all the "untapped" markets left, I think Louisville is the last option that major leagues would be interested in. Austin already got their MLS franchise so for arguments sake I took them off the table. That doesn't mean it will happen, but no one should be surprised if they are given a shot.