Keys was a vocal critic of Benitez during his time at Newcastle United. Benitez is understood to be the “No.1 choice” of Everton – who lost manager Carlo Ancelotti to Real Madrid earlier this month – following talks.
Keys claimed that many Evertonians were against the appointment because of Benitez’s previous association with Liverpool, the club he won the Champions League with in 2005.
“What a bad appointment,” the Qatar-based broadcaster tweeted. “I’ve already spoken to half a dozen guys who wore the shirt & they’ve all said the same thing ‘I’m done’. (Owner Farhad) Moshiri doesn’t understand Everton if he thinks this is a good idea. Evertonians will watch Tranmere.”
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Keys added: “If Benitez had any respect for himself or Liverpool he wouldn’t entertain the idea. Would Shanks (Bill Shankly) have done? (Kenny) Dalglish? (Graeme) Souness? (Roy) Evans? Any of them? Of course not.
"He left Newcastle exactly the same way – off to China when it suited him. Agent Benitez?”
On air, Keys said: “They could not make a more divisive appointment."
Former Everton striker Andy Gray, Keys’ longstanding broadcasting partner, said: “I would think the majority (of Everton fans) would not be happy.”
Benitez left Newcastle two years ago after failing to agree a new deal with owner Mike Ashley, who replaced him with Steve Bruce. Benitez and Ashley had been at odds over transfer spending and investment for 18 months.
The 61-year-old has been looking for a Premier League job since leaving Chinese club Dalian Professional early this year.
Benitez – who guided United to the Championship title in his first full season at St James’s Park – teased a return to the Premier League when he spoke about his future in April.
"In Spain, at the moment, it’s not possible to think about carrying out a project and trying to win something,” said Benitez. “In Italy and England, on the other hand, it can be done.
“It is still too early to know what will happen in the future, but it’s clear that Italy and England are places where I have been well.”