Liriano, 28, has compiled a 3-10 record with a 5.31 ERA in an up-and-down season for Minnesota, which is in fourth place in the American League Central, 13 games behind the first-place White Sox.
Known for his hard-breaking slider, Liriano is an impending free agent.
The Dominican Republic native has compiled a 50-52 record in 156 career games (130 starts) with a 4.33 ERA in his seven-year career with Minnesota.
He yielded three homers to the White Sox in a 7-4 Twins loss to Chicago Tuesday. But he also hurled a no-hitter against Chicago in May 2011.
In return, the Twins received pitcher Pedro Hernandez and infielder Eduardo Escobar, both of whom have made appearances with the White Sox this season.