The Blues have closely monitored the Burnley defender for several months, with Ronald Koeman admitting in January that he was interested in bringing him to Goodison Park.
However, they looked set to miss out on him this summer as both Manchester United and Liverpool were linked with his signature.
A return to Old Trafford seemed the most likely outcome, with reports suggesting Jose Mourinho was very keen on signing the former United man.
However, that interest now appears to have cooled with the Portuguese boss focusing his attention elsewhere.
According to the Independent, the Manchester United manager is intent on signing Benfica centre back Victor Lindelof and hopes to get a deal done following the international break.
As a result, Michael Keane is now seen as nothing more than a backup option by the club’s hierarchy should the move for the Sweden international not come to fruition.
With Liverpool targeting Virgil Van Dijk, and the Dutchman thought to be keen on the move to Anfield, that could leave Everton free to snap up Keane ahead of their rivals.
Of course, a deal will still need to be negotiated with Burnley, who are likely to hold out for big money for one of their key players.
But with United and Liverpool likely out of the running, it could make securing his signature a much easier prospect for the Blues than it had first appeared to be.