According to Matt Cerrone, the Sox asking price for Betts was 1 mid-rotation starter, 1 outfielder, and 2 top 100 prospects.
That's a pretty steep asking price. Even if the Sox waiver a bit on the whole "top 100" thing, there is no way to get anything close to that and include Price in the deal without paying so much money that it defeats the purpose of including Price.
If the Sox deal Mookie, it's best to do so in a package that nets them the best prospects, and if those prospects are MLB-ready, their minimum wage salary helps offset the cost of Price...