The Welsh international winger has been heavily linked with a world record move to Real Madrid in recent weeks.
"We very much want Bale to stay," Mills told the Evening Stadard "If a player is desperate to leave, it's very difficult to force him to stay.
"We've seen it in other clubs. Even if he has a contract, you can't force somebody to play for you."
Bale scored 26 goals last season on his way to being named PFA Player and Young Player of the Year.