Milwaukee is in a weird spot at the moment and frankly, it is unclear as to whether or not they are actually going to try and remain competitive in the NL Central. They already non-tendered Brandon Woodruff due to his shoulder injury and they traded away Mark Canha with Willy Adames and possibly Corbin Burnes also being on the chopping block as well.
However, the nice thing about the Brewers as a trade partner is that whatever path they choose, both involve them being active on the trade market. If they decide to make another run at a division title because the offers for Adames and Burnes aren't to their liking, the White Sox could offer a guy like Eloy Jimenez or Andrew Vaughn to give Milwaukee's offense a boost as their minor league system is pretty appetizing, If the Brewers instead starting selling players off, Chicago could be in the running to acquire some useful players at decent prices depending on how motivated Milwaukee is to cut their payroll.
The Cubs are seemingly mentioned everywhere in rumors this offseason. They are seemingly looking at the top of the market guys like Shohei Ohtani and Yoshinobu Yamamoto in the wake of the Cubs stealing manager Craig Counsell away from the division rival Brewers. The Cubs clearly are looking to make a splash and with their needs at the corner infield spots as well as on the pitching side, they could be in play for guys like Dylan Cease or Andrew Vaughn. Also, don't sleep on the Cubs getting involved for Luis Robert Jr. if they end up losing Cody Bellinger and they don't have complete faith in Pete Crow-Armstrong just yet.
The problem, of course, is that any deal with a cross-town rival is going to be tough to make. The optics of sending a quality player to the Cubs would probably not go over well with the White Sox faithful. However, it isn't like the White Sox have cared much recently about optics the last couple of years (the Tony La Russa debacle and basically all of the 2023 season come to mind as examples here) and the Cubs' do have some guys like PCA and Cade Horton that could be exciting pieces to build trades around.