Per Ken Rosenthal of The Athletic, Castro wants to be traded to avoid being "part of another rebuilding process the way he was with the Cubs."
Castro was dealt to the Marlins as part of the deal that sent Giancarlo Stanton to the New York Yankees last month.
The Marlins have been one of the most active teams this offseason. Stanton, Dee Gordon and Marcell Ozuna have all been traded as part of a front-office initiative to cut payroll.
In addition to Castro's desire to be traded, MLB.com's Jon Morosi reported on Dec. 28 the Marlins have also had discussions with teams about dealing outfielder Christian Yelich and catcher J.T. Realmuto.
Castro is signed for a total of $21 million through the 2019 season with a team option for $16 million in 2020, per Spotrac.
The 27-year-old Castro spent the previous two seasons with the Yankees. He posted a career-high .792 OPS in 112 games during the 2017 season.