Cueto, 36, joined the White Sox last month on a one-year deal worth up to $4.2 million and has made four starts at Triple-A Charlotte, posting a 5.17 ERA and 17 strikeouts over 15⅔ innings.
The White Sox hope Cueto, a two-time All-Star, will help stabilize their short-handed starting rotation.
"He pitches with style. He is a pitcher," White Sox manager Tony La Russa said. "We've gone against him when you look for this and he gives you that, or vice versa.''
Asked if Cueto could stay in the rotation, La Russa responded: "We would be disappointed if he's not, and we don't expect to be disappointed."
"He's done enough since he reported in Arizona, and what he's shown in Charlotte, we expect him to be helpful,'' he continued.
Lance Lynn, who pitched to a 2.69 ERA last season, is still recovering from knee surgery in April and hopes to rejoin the team later this month, while Lucas Giolito is currently on the COVID-19 injury list and also missed two starts last month because of an abdominal strain.
The Associated Press contributed to this report.