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."
Davis believes the former England Under-19 international could be the perfect replacement for former skipper Luke Murphy, who joined Leeds earlier this summer.
He added: "The quality, creativity and goalscoring ability he's got was apparent to everybody. He's the creative player that Murphy was and we could do with that type."