Latics chairman Dave Whelan has admitted he expects the forward to complete a move to Goodison Park in the next 24 hours, while defender Antolin Alcaraz is poised to follow suit on a free transfer.
Ivory Coast international Kone, who has also been linked with Swansea and Norwich, arrived at Wigan from Levante last summer and scored 11 goals.
He also helped the club secure the FA Cup for the first time but confirmed his desire to leave following relegation to the Championship.
"You always have ambitions as a footballer, and I don't intend to play in the English second division," Kone was quoted by The Sun.
"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.
"I've had plenty of approaches, I can't reveal the names of the clubs. But Crystal Palace have gone up, and from the moment a club is in the Premier League that is good for me.
"I'm under contract with Wigan for two more years. But if there is an offer that is good for both me and Wigan I will seek to leave."
Wigan, meanwhile, are closing in on goalkeeper Scott Carson and Newcastle defender James Perch.