Aneke, 20, scored eight goals during two loan spells with the Alex last season and Davis is keen to do another deal for the Gunners midfielder.
"I've had dialogue with Chuks, he's been in Asia. So we'll just check out that position there," he told BBC Radio Stoke.
"He did terrific for us last season. I think initially people didn't see his quality, but over time he came to fruition and his fitness was much better."