Martinez's future hangs in the balance as the Toffees, with two league victories since February, have endured a miserable Premier League season.
With a squad that good, it has been suggested by the fans that they certainly should be a lot higher in the table than 11th and the Spanish coach, whose side also bowed out of the FA Cup following last week's semi-final defeat by Manchester United, may be on borrowed time.
Consequently, speculation is rife that the Merseyside club have drawn up a shortlist of potential successors at Goodison Park - and the ex-Liverpool boss is on it, say The Mail.
Many Evertonians certainly want a new man in charge, but would they take the former Reds coach?
@LivEchoEFC I know he called us a small club but he is a very good manager— ken jones (@kjon64) May 3, 2016
Even if it were true, whether EFC fans wanted him or not there's no way Benitez would come to us. He'd see it as betrayal.— RobertoFoolofScience (@Bluenose69) May 3, 2016
Benitez's long-term future at Newcastle perhaps hinges on whether the Magpies survive relegation this season. With two games left, Newcastle are 17th in the table, one point above the drop zone but Sunderland and Norwich City, in 17th an 18th place, have a game in hand.