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Benitez, who succeeded Carlo Ancelotti in the summer, watched on as Liverpool thrashed Everton 4-1 at Goodison Park on Wednesday.
Everton have now lost seven of their last 10 Premier League matches under Benitez, with their last league win coming against Norwich City in late September.
Benitez has received the backing of Everton majority owner Farhad Moshiri, but the Spaniard could be on the chopping block if results don’t swing in his favour.
The Toffees languish in 15th place and are only five points clear of the Premier League relegation zone.
The Daily Mirror now reports that Mourinho could be lined up as the next Everton manager if Benitez is axed from Goodison.
Mourinho was sacked by Tottenham back in April and would later replace Paulo Fonseca as Roma manager ahead of the current Serie A season.
The Special One’s second spell in the Italian league has seen disappointing results for Roma, with the Serie A club nine points adrift from the top four.
And Mourinho endured a tough night on Saturday as former side Inter Milan convincingly beat Roma 3-0 at the Stadio Olimpico.
According to The Mirror, the former Manchester United and Chelsea manager might ‘find it hard to resist’ the chance to return to the Premier League with Everton.
Benitez believes that Everton can weather the storm going into the second half of the season and remains “positive” amid uncertainty over his future.
“I have experience in situations like these, to fight for titles and to try to avoid relegation and my experience is telling me to stay calm, to keep working hard, to try to correct the mistakes, then keep going,” he said.
“What we want is to stick together because that is crucial. It is a frustrating time for us, but we have to keep going and work really hard.
“When you are in a bad run, every game feels ‘must win.’ I am positive and still have the belief we will do well because we did it at the beginning of the season.
“I said a lot of times that we will do well in the second part. Now is a time for us to stick together and try to go to January in the best possible position.”
Everton will host Arsenal at Goodison on Monday, with kick-off scheduled for 8pm UK time.
Featured Image Credit: PA
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