Benitez will be out of work this summer after doing a superb job at Chelsea on an interim basis this season.
Real Madrid have been linked with a move for the former Valencia boss but Carragher has not ruled out the chance of him staying in the Premier League and going to Goodison Park.
Carragher was an Everton supporter as a boy and will play his final game in a Liverpool shirt this Sunday at home to Queens Park Rangers.
The Liverpool legend doesn’t see the problem with Benitez managing both Merseyside clubs in his career and expects his former manager to stay in England.
“He wants to stay in the Premier League and he’s stated that a few times, that is his priority.
“It might ruffle a few feathers, with the Liverpool and Everton side of it. I don’t know how difficult that sort of thing is. I don’t think it’s happened before with managers.
“I know it happened between Tottenham and Arsenal with George Graham and I think eventually it was a problem for him.
“Everton would love to get someone with his CV, but with the Liverpool situation it makes it difficult. If all parties come together and they are willing to give it a go then I’m sure he would do a good job.”
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