Chester joined Villa for £8m from West Brom, and according to the 'Daily Mail' Villa still owe part of the player fee to them.
Villa are still in talks over Jack Grealish with Tottenham and Birkir Bjarnason with Middlesbrough.
Jonathon Kodjia and Conor Hourihane could also be sold to help Villa with their financial situation.
Villa will need to make player sales in order to help them pay off their tax bill and other outstanding payments.
Stoke have also shown an interest in Huddersfield Town winger Tom Ince.
In the meantime, Stoke midfielder Badou N'Diaye is looking to speed up his exit, by not reporting for pre-season training on Wednesday.