The Los Angeles Dodgers have tried to trade Yasiel Puig before.
There was that time they tried to send him to the Milwaukee Brewers for Ryan Braun in 2016. More recently, they offered him to the Washington Nationals for Bryce Harper in July, according to Jorge Castillo of the Los Angeles Times.
If there's anything to be gleaned here, it's that the Dodgers are very much open to dealing their star right fielder as long as they get a better player back.
So, why not offer him* to the Miami Marlins for J.