The winger is also attracting interest from Liverpool, Arsenal, Stoke City, West Ham United and Middlesbrough.
Everton fans made their feelings for the Scot perfectly clear on Twitter.
It is being reported that Liverpool have decided against offering the 35-year-old Ivorian new terms despite his considerable role this season.
The 27-year-old left the Scottish Premiership side for Hibernian on loan.
Michail Antonio only joined the Hammers last summer.
HITC Sport understands Brentford eye former Everton midfielder.
Aston Villa are reportedly interested in Roberto Martinez.
The 24-year-old labelled the Leeds supporter a "muppet".
Glasgow Rangers are now unlikely to bring Hibernian star Jason Cummings to Ibrox.
There were suggestions that Michael Carrick was set to leave Manchester United.