The Colorado Rockies, who employed Ottavino from 2012 to 2018, are also open to bringing the right-hander back.
Interest in Ottavino extends beyond those three teams as multiple other clubs are considering him, a source told Morosi.
Earlier in the offseason, it was reported that Ottavino was high on the priority list for the Red Sox. Boston re-signed Steve Pearce and Nathan Eovaldi, but the team could lose closer Craig Kimbrel, and right-hander Joe Kelly has already left after agreeing to a three-year deal with the Los Angeles Dodgers.
Kimbrel is reportedly looking for a six-year, nine-figure deal which would set a record for term and total value among relievers. Meanwhile, Boston seems resigned to waiting for Kimbrel's next move before signing another relief pitcher.
The White Sox, on the other hand, moved on from Joakim Soria, trading him to the Milwaukee Brewers partway through the 2018 season. Despite finishing with 100 losses, Chicago's bullpen was middle-of-the-pack in 2018 with a 3.99 FIP thanks to Soria, Jace Fry, and Aaron Bummer.
Ottavino, 33, is coming off a career year when he authored a 2.43 ERA and 2.74 FIP with the Rockies. Over 77 2/3 innings, the right-hander struck out nearly 13 batters per nine innings while notching six saves in a setup role behind Wade Davis.