The Ivorian centre-back was snapped up by the Black Cats from Lorient over the winter when their status in the Premier League appeared to be under serious threat.
And Kone made an immediate impact under then manager Sam Allardyce, slotting in at the heart of the Wearsiders’ defence to help guide the North East outfit clear of the drop.
Reports claim that this has alerted Everton, who have set the wheels in motion to lure the 27-year-old to Goodison Park.
It’s understood that, despite his importance at the Stadium of Light, Sunderland are likely to accept a serious offer for the defender, with the club burdened by one of the smallest budgets in the top tier as they look to build under David Moyes after Allardyce’s exit.
Kone could be an eventual replacement for John Stones, who has been linked with Manchester City of late.