West Ham have been transformed of late picking up seven points in a week from tough fixtures against Chelsea, Arsenal and Stoke City.
Everton are sitting ninth after going unbeaten in the six games they have played since Sam Allardyce was appointed boss.
Everton and West Ham are considered the two biggest clubs outside the established Premier League top six.
And their revival under Moyes has caught the attention of world champion boxer and ardent Toffee Tony Bellew, who will have recruited another legion of fans after tweeting praise for the Hammers following their 3-0 win at Stoke last time out.
"Happy to see West Ham doing well!" Bellew posted on Twitter.
"Wouldn’t wanna see any of the big clubs going down and also good to see Moyes doing well."
Happy to see West Ham doing well! Wouldn’t wanna see any of the big clubs going down and also good to see Moyes doing well..— Tony Bellew (@TonyBellew) December 16, 2017
Moyes was only handed a six month contract with the Hammers initially but he looks set to be handed an extended deal if the club continues on an upward curve.
Bellew will also find himself with a larger following than usual when he takes on Millwall fan David Haye in their much-anticipated rematch on May 5th next year.
Ironically a week later West Ham entertain Everton at the London Stadium in the final game of the season by which point both clubs will be hoping they are home and hosed.
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