Manuel Pellegrini's side will only make a move when Spurs do however.
The midfielder was again in impressive form for the Blues last season despite their struggles, as he was the season before when he flourished in Roberto Martinez’s first year at the club.
Those performances have garnered a lot of interest in the former Wigan man, with Tottenham thought to be chief among them.
According to The Mirror, they have monitored his progress closely over the past year and manager Mauricio Pochettino is expected to lodge a formal offer within the next fortnight. Manchester City meanwhile, will reportedly only make a move when Spurs do, likely a tactic to work out how much he may end up costing.
It is believed that it will cost as much as £20million to sign him from Goodison Park, with the Toffees clearly likely to be very unwilling to part with one of their key players ahead of the new season.
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In fact, the rumours of a move seem to be coming from suggestions that the Republic of Ireland midfielder is unhappy at his current club, with the root of the problem seemingly that he has not been offered a new contract despite his form, as suggested by the Daily Mail.
Surely then, if the rumoured interest turns into something concrete, Martinez and his side will move quickly to offer the midfielder better terms to tempt him into staying at the club.
So far though, there have been no suggestions from the player that he is truly unhappy and it would certainly take a big some for Everton to part ways with their man at this moment in time.