The England international has 18 months left on his current contract with Villa and has recently been linked with the likes of Manchester United, Liverpool and Tottenham.
“It’s a triumph if we keep Ashley for next season and it’s a show of intent by everyone here that we want to keep our best players,” McAllister told the Daily Star.
“If we keep him, it will mean Ash thinks he can win things with Villa.
“Hopefully, by the signings we have made we can convince our top players to want to be here.”