With Latics having slipped out of the Premier League, a number of high-profile departures are expected from the DW Stadium this summer.
Kone is among those being tipped to make the step back into the top flight, with the Ivorian having shone during his debut season in England.
He netted 11 times in the Premier League last season and is reported to be among those Roberto Martinez is hoping will follow him from Wigan to Everton.
Kone is, however, focused on his international commitments at present and insists he has no intention of rocking the boat by pushing for a move.
He said: "I have a contract until 2015 with Wigan and I settled very well there. It is a brilliant community football club. The chairman is fantastic.
"Yes, I want to be playing in the Premier League but it also depends on Wigan because I have a contract with them.
"Everton? Just because the gaffer is in charge makes the link stronger but, to be honest, I don't know what will happen. After the international games I will know more."