The England international has been linked with the likes of Manchester United, Liverpool and Chelsea.
The 25-year-old has just one year left on his current contract at Villa Park.
“We are doing everything we can to keep Ashley Young,” said McAllister.
“He has got a year left of his contract so we are still holding the aces but we appreciate that there are people interested.
“It’s been well documented but Aston Villa are trying to keep him here.”
