Gallardo is all but ready to return to Milwaukee in 2018.
The Cubs are the latest team to throw their hats in the ring for the right-hander.
The Braves received Brandon McCarthy, Scott Kazmir, Charlie Culberson and Adrian Gonzalez in the deal.
Sabathia will return to the Yankees in 2018 for his 10th season with the club.
Fowler is pursuing a lawsuit against the White Sox after sustaining a season-ending knee injury last June.
Martinez wants to be more than a designated hitter in 2018, but that may be off-putting to his biggest suitor.
Koehler is expected to feature in the Dodgers' bullpen in 2018.