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The ex-England boss, who has had spells at both clubs himself, believes that the Spaniard’s naturally defensive approach won’t play out too well with the Toffees’ fanbase – especially if results don’t always go his way.
“I have seen there are a lot of Everton fans unhappy about the situation because of the rivalry between the two clubs [Everton and Liverpool],” he told Sky Sports on Monday morning.
“Rafa’s track record is very good, in terms of the time he has had as a manager. But I have to say, if you call me a defensive-minded coach then Rafa’s exactly the same as I am.
“He bases his performances on clean sheets and building from there and he has done that throughout his career.
“So, if they are talking about open and expansive football then I don’t think that’s the case with employing someone like Rafa.
“I think that will come eventually, depending on what players they let go and bring in.”
However, Allardyce does believes any ill-feeling towards Benitez from Everton supporters will subside if he can get the Toffees performing at a high level and consistently winning matches.
He said: "The fans are on your side when you start winning, that is what it is all about."
We’ve gathered the best of today’s Premier League transfer speculation below...