The 22-year-old striker is out of contract in the summer, and there is no imminent agreement with the club.
Hutton does not want to see Davis leave, and hopes manager Dean Smith will intervene.
Davis has scored against Crewe Alexandra in the Carabao Cup for Villa this term.
He told Football Insider: "There's other boys, like Keinan Davis, I think he's out of contract. He's one I would be desperate to tie down even though he's had his injury problems this season.
"I think he's got everything to be a top centre-forward. It's just as a club where you see them in the future."