Neighbours Liverpool have also been linked with the Japanese international who looks set to leave Russia in the summer as his contract comes to an end at the end of the year.
The Merseyside duo will have to lock horns with clubs from Spain and Italy to ensure the 26 year old comes to the Premier League before the start of next season.
CSKA will not want to lose their star man for free next January and so may look to take whatever they can for him in the summer.
Honda has revealed he won’t be signing a new deal in Russia and so Moyes will look to make his move swiftly.
The Everton boss will want to sort his own future out before making any summer additions but Liverpool are set to pounce if the Toffees cannot pull their finger out.
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