I think it depends on what you think a big time coach is. Being in the SEC or BIG is a massive advantage nowadays. If you look at the ACC and Big12, there might be someone out there. Here are probably the 3 best that UK could land:
Matt Campbell is having a good year at Iowa State and has very strong Ohio connections, but he’s had some very mediocre years at ISU.
Chris Klieman is having a pretty good 3rd year in a row at Kansas State. Crushed it at the FCS level with 4 national championships in 5 years and has gone 10-4, 9-4 and currently 7-1 in the last 3 years.
Rhett Lashlee at SMU is in his 3rd year and has gone 7-6, 11-3 and currently 7-1 in his 3 years there. Offensive guy for those that want that side of the ball.
Big time as in proven winner at P5 level.
I like Cris Klieman. Lashlee is an up and comer as well. I think
Mike Gundy, Oklahoma State is a possibility. Things are stale in stillwater and a change may do him good.
Pat Narduzzi at Pitt can flat out coach.
Bill O'Brien Boston College. - nfl, Penn st... etc... etc
Curt cignetti: what a baller this guy is
Jon Sumrall - young up and comer at G5 level, alumni, stoops protege . de facto pick of the deep state ( mitch and his flunkies), could be a good one but is he best available? How many alumni work out when they come home? ( Joker)
Dan Mullen, did well at Florida and had Missi St. At #1. Dood can flat out coach. Unfairly ousted at florida
Unrealistic :
but you still talk to Chris Peterson, Nick Saban, urban meyer, bill bellicheck just to show you are confident about hiring the best available and discuss with them how they built their respective programs and who they would suggest.
You talk to some nfl guys as well, interviewing successful coordinators. However you do it, you build buzz, need to get the boosters and fans fired up to donate NIL