The Chicago White Sox could really use a pitcher of Trevor Bauer’s caliber. In fact, every team in baseball needs a pitcher of this caliber. The White Sox might be able to make it happen if he was someone they wanted to bring over. He has plenty of experience dealing with Chicago as he has been in Cleveland for almost his whole career. He is on an expiring contract which makes his value worth a little less so the White Sox might be able to get away for not giving up as much.
If they made this trade, it would be the Reds adding a pretty good everyday player and a prospect for Bauer. Matthew Thompson is a right-handed pitcher that expects to be in the MLB by 2023. He is only 20 years old so he has a long way to go before he is truly ready.
As for Adam Engel, he is a really good defensive outfielder. His offense gets hot and cold but he is a premier bench guy on a winning team. If the White Sox keep him, he will often be in the outfield late in games which is valuable for a lot of teams trying to win. It wouldn’t be awesome to see him go for White Sox fans but for a pitcher like Bauer you have to.