The White Sox and Abreu have discussed a long-term agreement, reports ESPN's Jeff Passan.
Abreu has been one of baseball's most consistent run producers since arriving from Cuba as a 27-year-old rookie in 2014. In all but one season, the 32-year-old has driven in at least 100 runs while belting 30 or more homers in four different campaigns.
But even with his strong offensive numbers, Abreu is "facing a tough market for aging first baseman - and has a qualifying offer attached to him," Passan writes.
Abreu was extended a $17.8-million qualifying offer Nov. 4 and has 10 days to accept or decline.
The White Sox have made it known they'd welcome back the All-Star slugger, who has a strong presence in the team's clubhouse and is viewed as a leader to Chicago's other Latino players.
"With Jose, we've heard his thoughts that even if we don't re-sign him, he's going to re-sign himself. We've heard (team chairman Jerry Reinsdorf's) thoughts about (how Abreu's) always going to wear a White Sox uniform. I don't think they are going to be teaching this in negotiation classes in college any time soon (with) how this one is unfolding," White Sox general manager Rick Hahn said in September, according to Vinnie Duber of NBC Sports Chicago. "But my takeaway from all that is that there's a strong desire on both sides to figure out a way to keep Jose in a White Sox uniform beyond this year."
Abreu also mentioned his affinity for the White Sox in July when he explained that he didn't want to leave a team that's building "something big," according to Duber.
The White Sox took steps in the right direction in 2019, finishing with a 72-89 record compared to a 62-100 mark in 2018.