Rangers boss has been touted as a shock replacement for Carlo Ancelotti after the legendary boss jumped ship for Real Madrid.
It's an appointment that would be difficult given Gerrard's status as an Anfield idol. The notion was dismissed by Rangers legend Ally McCoist, and Barnes is of a similar frame of mind.
Gerrard has made no secret that his dream is to manage Liverpool and the former Celtic boss believes that would see him snub Everton.
Barnes told Bonus Code Bets : "At this moment in time, Steven Gerrard won't move to Everton. If he harbours any ambition of becoming Liverpool manager in the future, which I believe he does, I don't think moving to Everton would be a good idea for him in terms of ingratiating himself with the fans..
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