Sky Sports revealed on Tuesday that the Toffees had made an approach, with Roberto Martinez planning a raid on his former employees.
Kone has been linked with a switch to Goodison Park ever since it was confirmed that Martinez was to leave the Latics for Merseyside.
He has a £5million buy-out clause in his contract and is looking to activate that following Wigan's relegation out of the Premier League.
Everton are prepared to offer him an immediate return to the top flight, but they face competition for the Ivorian's signature from two other clubs.
Whelan said on a possible deal: "Three clubs have made offers for Kone - Everton is one - as he had a clause in his contract that he could go if someone paid £5m.
"I think he will go to Everton."