Jay, 33, has career marks of a .285 batting average and .352 on-base percentage. He split time between the Royals and Diamondbacks in 2018, hitting .268 with three homers, 40 RBIs, 74 runs, .330 on-base percentage and .678 OPS in 143 games.
Jay is a close friend of star free agent Manny Machado, whom the White Sox have aggressively pursued. The White Sox have formally made Machado an offer. Those two and White Sox first baseman Yonder Alonso, who's Machado's brother-in-law, frequently work out together in the offseason.
Jay's deal is pending a physical.