With their relief corps still a work in progress as spring training draws closer, a deal for the right-hander would figure to bolster the back end of the Blue Jays’ bullpen.
Roberto Osuna and Jason Grilli are Toronto’s only two locks for high-leverage duties. Joe Biagini had a productive rookie campaign a season ago, but it is unclear whether he will remain a reliever or be stretched out as a starter to open the season.
Robertson saved 37 games for the White Sox in 2016, posting a 3.47 ERA in the process. The 31-year-old has registered 110 saves over the past three seasons.
The former all-star is signed through 2018 and has $25 million remaining on his contract. Chicago is currently undergoing a rebuild, having already moved ace Chris Sale and outfielder Adam Eaton during the off-season.
Blue Jays pitchers and catchers are scheduled to report in Dunedin on Feb. 22.