The 29 year old Ivorian international has made no secret of his desire to leave the Latics following relegation to the Championship.
Just last week Kone, who scored 11 goals last season, said: “You always have ambitions as a footballer, and I don’t intend to play in the English second division.
“Wigan have gone down, which is a real shame. It’s up to them to set out their stance about my situation. I aim to play for one of the best clubs in England, and I hope I will get the chance.”
The major stumbling block surrounds Everton's desire to pay for the striker in installments rather than the anticipated £5 million fee up front.
Should Kone leave new manager Owen Coyle has targetted unsettled Norwich City striker Grant Holt as an ambitious replacement.
The 32 year old is presently unhappy with his situation at Norwich and is looking for a move away from the Canaries.
A fee in the region of £2 million is being quoted with Holt set for a drop in wages to return to regular first team football with the Latics.