Abreu is not leaving the White Sox the only way he is leaving is if the White Sox don't offer him a contract and then he may just retire instead of playing for another. All rumors that I have seen or heard say he wants to stay with the White Sox and the feeling is mutual with the White Sox. So Abreu is not really an option unless the Brewers want to pay him $20m+ for the next 4-years. That is basically the only way the Brewers would be able to get Abreu and even then I don't think he leaves the White Sox.
I don't believe the Brewers will play in FA this off season I believe what the Brewers have now is what they will go with next season. Basically Frelick and Turang will be the additions at 2B and CF. Ruiz may serve as the 5th OF. That means Peterson, McCutchen, Wong, Narvaez and others will not be back for 2023. The best option to improve for 2024 would be to trade one or both of Burnes and Woodruff.
I think the Rangers, Tigers and Orioles make the most sense here as they have the prospects to make the trade for either. I put what I thought the Orioles could give up in a package for Burnes. Both of the trades for Burnes from the Orioles would be for 2023 and beyond as they have two prospects who are ready in AAA right now. I am just not sure the Orioles make the trade as they would be gambling on competing in 2023 and 2024 in the AL East. It is possible but that is a huge gamble though the Orioles would definitely be able to extend Burnes by giving him a rather large contract to stay beyond 2024 as they basically don't have anyone on the books right now. The Orioles could add $85m and they would be at about what the Brewers are at so if they offer Burnes a 5-year $140m deal I think he accepts that as it is basically the same deal DeGrom signed in 2014. The Orioles would still have $57m left to spend on other free agents and increases to their own players.
The Red Sox are also another interesting team to watch but I don't like any of their prospects in a Burnes or Woodruff trade. Lauer or Houser though some of their prospects would be good to get in a trade. The Mets would also be a team that I think sneaks in but I don't think they would give up Baty plus more for Burnes.
For a Mets trade I think this makes the most sense:
Brewers get:
Baty (3B), Mauricio (SS), Ramirez (OF), Vientos (1B) and Ziegler (RHP). This would give the Brewers their future 3B in Baty for 2023 and a future 1B/DH in Vientos in 2024. Ramirez and Ziegler are the furthest away.
With the Rangers recent shakeup in their front office I am not sure they make a trade for Burnes. If they would have given their GM another year then yes I think they definitely make the trade for Burnes or Woodruff. The Rangers really need some pitching and maybe they get desperate with how much they spent this past offseason. I am just not sure how much the Rangers can spend and I think if they do trade for either Burnes or Woodruff they will want to be able to extend them. I think Woodruff would be the cheaper option to extend and Burnes it would take a DeGrom like deal to get him to sign and you would be basically just buying out the two arbitration years and three free agent years.
I think Burnes and Woodruff will definitely be the hot topic names this off season for the Brewers. If Burnes or Woodruff are not traded then I think Lauer/Houser and Adames/Renfroe are probably moved instead. I think Houser and Renfroe would be the two options the Brewers would prefer to trade as they have replacements for both in Small and Wiemer. There really isn't a replacement at 3B and if the Brewers are trading players away then free agency wouldn't be an option. Well it would be someone like Peterson being signed to platoon with Brosseau at 3B. Urias would then move to 2B and Turang takes over at SS in this scenario.
The Brewers are in a difficult position this coming off season. They need to make a move and don't really have the funds to play in FA and nor should they.