I can't remember where I read it but it was a few years ago now, you can google it and probably find something. They get 32 teams in. The majority if your conference winners win the tournament, maybe 4 or 5 small schools don't,and then maybe 4 or 5 bug conferences don't, so that's 10 teams that get in via conference winners, and I'd say that's a bit high. That leaves you 22 teams, if you don't think Tennessee would be one of the 22 best teams left out of the NCAA tournament or one of the 22 best at selling tickets then you are in denial.
Little side note, former ut coach don devoe is on the selection committee for nit, can't hurt I guess.
Edit: most years except last there have usually been 5-8 auto qualifiers, so thatd make it 24-27 teams that get at large bid. Once again if you don't think UT would be a top 30 team/ticket seller you're crazy. Now if they go 0-4 ok, but finishing 2-2 which honestly should be a minimum and they'd be in.
Also statsheet currently projects Tennessee at 14-13 in the NIT as a 7 seed
TIFWIW