Marco Silva is under extreme pressure to keep his job with the Toffees.
They put in a spirited display against Leicester City on Sunday, but lost 2-1 after conceding a last-minute goal.
Benitez, who is managing in China, is among the bookmaker favourites for the job.
Speaking on beinSPORTS, Gray said about Benitez: "I don't want him. He's a pragmatist. I think Everton need someone who's going to inspire them.
"Somebody needs to come in and lift the place. I don't think Rafa would lift the place.
"He would stabilise it, but I watched Newcastle last season, you wouldn't want to watch that every week."