If they're not under contract for next year, they need to be traded, even if you have to cover the entire salary to get back a C- 25 year old in low A. If you don't trade them, you have to pay the salary anyways, so you may as well get back something.
If the offer is good enough, I would also trade anyone not under contract for 2023, especially given the non-zero chance of a work stoppage next year (maybe contracts will not apply, maybe they will; I don't know enough to say for sure).
What I'm really worried about is that the Twins go 11-4 out of the break, and the front office decides not to trade, only to have things fall apart in August (consecutive series against HOU, CWS, TB, CLE, NYY, BOS, and MIL; once the Twins finish playing STL on 8/1, they don't get another game against a team with a losing record until 8/31).