Newly-appointed Latics boss Coyle is resigned to losing the Ivorian following Wigan's relegation to the Championship under Roberto Martinez, who wants to bring Kone with him to his new challenge at Goodison Park.
Coyle has revealed that several clubs have bid for Kone, who apparently favours a reunion with Martinez, and that the 29-year-old's exit from the DW Stadium could be completed in the near future.
"I'm led to believe through his representative that Everton is the club he wants to join," Coyle told BBC Radio 5 live.
"It's not rocket science to say that Arouna Kone will probably leave at some point this week. There have been a number of offers in for him.
"There is no problem, he goes with our blessing because I need players who need to be at Wigan. If his heart's elsewhere then he's no good to me."
Kone scored 13 goals in 36 appearances in all competitions for Wigan last season following his arrival from Levante.