Probably won't happen until August, so don't get your hopes up. As much as the Twins aren't good, even at 46-48 they're two games back of the White Sox who also, just aren't very good, and are in first place. The AL is terrible but it's letting under .500 teams fart around relevancy and they're just not selling until the last moment or they go on ten game streak of dropping eight of them.
If you want an early deadline deal it's basically: Royals, Angels, Orioles, Mets, Rockies, Giants as your shopping spots as I think all of these teams are way out of it and probably aren't going to convince themselves they're getting back in. Boston probably belongs here but I don't think they're going to throw in the towel mentally yet, same with the Padres. It will also allow these teams to ask for significant overpays.
Your fringe teams like the Tigers, Twins, Red Sox, Padres, Blue Jays, Nationals (as examples) will be happy to float along for a few weeks to see if they can have the opposite of the situation above with the Twins; a good eight of ten run that puts them in buying positions.
As for the Cubs, they're probably going to wait a few weeks too. They'll let the Angels or the Giants get a little more uncomfortable to hope for a Detmers or Webb trade, allow Taillon, Palencia and maybe Cabrera get back up and running and then assess.