Jose Abreu is an elite offensive first baseman. He has been the White Sox best player throughout some very dark times. The fact of the matter is that he is on an expiring contract so he is always going to be in trade rumors. The White Sox might opt to keep him and resign him to be there as a big bat in the middle of the lineup and be a veteran presence on a young team.
The White Sox could also decide to move him because teams would pay a premium to have his services for the playoffs. He is an elite hitter having one of the best years of his career. He currently has a .279 batting average with 22 home runs and 72 RBIs. A 30 home run and 100 RBI season is very much in play for Abreu. He would look nice in the middle of a lot of Major League lineups.
There have been rumors out there connecting him to some east coast teams along with some teams out west, but nobody actually knows where he would go if Rich Hahn decided to move him. Most fans and people in the organization would probably give backlash if they moved him unless they got an offer they couldn’t refuse. He has meant a lot to this team and its fans over the years so seeing him be traded would be tough.
With all of that said, if you had to pick three players that are the most likely to be traded, Abreu would have to be one of the three you pick simply based on the contract and age situation. The ideal situation would be that Abreu gets to see this rebuild through and be the old guy that every championship team needs.