The Ivory Coast striker impressed for Wigan last season despite their relegation from the Premier League and his 13 goals caught the eye of Liverpool boss Brendan Rodgers.
Everton chief Roberto Martinez knows all about him following his time in charge at the DW Stadium and a battle between the Merseyside rivals could be on the cards.
Kone is keen to get back in the Premier League and would also consider a move to Crystal Palace, who have also been heavily linked with the £10million rated striker.
"You always have ambitions as a footballer, and I don't intend to play in the English second division," Kone revealed. "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."