What is the key in the return for Jays assuming they move a catcher? Is relief help the goal? Are prospects okay?
I think Jansen is the guy that ultimately is moved. He has got great ability and has been so productive when he's on the field but just seems to be more injury risk than with Moreno/Kirk.
I know the White Sox like Jansen a ton. They don't love Grandal's health and don't think he works well with pitchers. He can actually fit the Jays pretty well provided they swap bad contracts on Ryu. At least a Grandal addition could insulate against a Kirk/Moreno injury, keep Moreno positionally flexible and potentially be a big add at DH/1B with the lack of lefty presence in the middle of the lineup. Grandal was absolutely incredible down the stretch in the second half of 2021. The success wasn't that long ago despite a brutal 2022. Secondarily Biggio fits the White Sox really well as a complementary piece.
However, outside of relief help, not sure the White Sox have much to offer in terms of players that can contribute at the MLB level immediately. Hendriks would be a great fit with the Jays if they're hesitant on Romero after his season ending. Hendriks is an elite closing option. Otherwise, Graveman is a good vet option but obviously carries less value than Jansen. Aaron Bummer has been an outstanding lefty set-up when healthy but has had health issues in recent seasons. That said, his contract has the potential to have tremendous surplus value with limited downside if his arm falls apart (2 reasonable team options).
The teams could swap bad contracts on Ryu and Grandal. The Jays could use Jansen to bolster the pen. Unless the White Sox are willing to part with Hendriks (they're hesitant), the issue to me is whether the Jays are fine with taking back prospects to even out the value. White Sox could add most likely AAAA guys that could possibly be decent players (3B Jake Burger, 1B/DH Gavin Sheets) but these guys are probably better suited with rebuilding squads and probably don't move the needle too much.