MLB Network reported the Cubs are still pursuing Gray, mainly because he (like Quintana) would be under control beyond 2017.
The pitcher has a 4-8 record this season, with a 4.49 ERA and 109 strikeouts in 104 innings of work, and he'll be looking to continue his strong pitching of late as the Cubs get the second half of their season underway.
For Quintana, White Sox received the Baseball America's No. 1 prospect Eloy Jimenez, a power-hitting outfielder, and No. 2 prospect Dylan Cease, a 100-mph right-hander, from the Cubs, along with minor-league infielders Matt Rose and Bryant Flete.
An All-Star in 2015, Gray has struggled with injuries over the last few seasons - making just 22 starts in 2016 with a 5.69 ERA.
The Cubs, who now sit below.500 at 43-45, now rank fifth in the National League in team ERA at 4.10, but have failed to receive consistent performances from usual stalwarts such as Jon Lester (5-6, 4.25 ERA), Jake Arrieta (8-7, 4.35 ERA) and John Lackey (5-9, 5.20 ERA).
Mike Montgomery and Jake Arreita are scheduled to start the first two games for the Cubs.