I think he would not fit in well there. Like part of his allure in recruiting is the conference. Not sure he would be able to recruit anywhere close to UK levels in the Big Ten West. Especially with USC and UCLA coming in.
Stoops would be a perfect hire for a school that is P5 in a weaker conference.
The problem is with conference realignment, he doesn't have time. He is at a point where he accepts his place at Kentucky or he takes a jump / chance at a job like Auburn (if interests from Auburn) or another job with opening that is an upgrade over UK.