The Chicago White Sox might not be done yet.
It's unclear whether one of the two outfielders would still be in play for Chicago after committing $12 million to Encarnacion.
Puig is apparently the team's primary target, Mark Feinsand of MLB.com reports.
The 29-year-old Puig spent the first half of the 2019 season with the Cincinnati Reds before a midseason trade to the Cleveland Indians. Over 149 games, the former All-Star hit .267/.327/.458 with 24 home runs and 19 stolen bases.
The Miami Marlins have also expressed interest in Puig.
Castellanos, 27, split last season between the Detroit Tigers and Chicago Cubs, and he enjoyed a second-half breakout after being dealt out of Motown. In 51 games with the Cubs, the outfielder hit .321/.356/.646 with 16 homers and 21 doubles.
A report recently surfaced suggesting that Castellanos preferred to go to a team that's building a winning culture, like the Cubs, San Francisco Giants, or Texas Rangers.
The White Sox busy offseason has already included one outfield addition in Nomar Mazara, who was acquired via trade from the Texas Rangers. Mazara, like both Puig and Castellanos, has primarily played right field in the majors.