The 22-year-old Scotland international is wanted by Nottingham Forest and has expressed a desire to leave.
Sky Sports says he handed in a formal request for a transfer and it was turned down.
Several English clubs have wanted McKenna in the past few transfer windows, but Aberdeen have remained steadfast in their refusal to sell.
It is unclear if anything will change in the last few days of the Premier League and Championship transfer window.
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!