The 66-year-old, who has also spent time with both the Magpies and the Toffees, argued that the Spaniard could face an uphill battle at Goodison Park, not only because of his connections to bitter rivals Liverpool, but also because of his conservative tactical style.
Benitez has been heavily-linked with a move to the blue half of Merseyside, with various reports suggesting that his arrival could be imminent.
For his part, Allardyce spent six months in the Everton dugout, and has claimed that the club’s supporters would ideally prefer a more attacking coach.
“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.
"I'm sure there are a lot of Everton fans who are unhappy with the situation because of the rivalry with Liverpool. Rafa's track record is very good.
"You can talk about the style of football that you play, first it is winning and then winning and playing well is the ultimate goal.
"The style of football is talked about so much, it overshadows what is more important, winning matches and finishing up the league to match the expectation and money spent."