As exclusively revealed by Goal.com, the FA Cup-winning boss is the Toffees' top target after David Moyes agreed to join Manchester United in the summer.
|10/3||Roberto Martinez is 10/3 with PaddyPower to be the next permanent Everton manager
"It is something we face every year and, if we do get relegated, he may decide he wants to stay in the Premier League but he may decide he wants to stay with Wigan because he is a great favourite here," Whelan told Sky Sports, speaking before Tuesday's game against Arsenal.
Asked if the Toffees had made an approach for Martinez, the 76-year-old said adamantly: "No. Everton would never do anything like that until the end of the season.
"Bill is keen on his football and is a total gentleman, so he would never do that until we know what our destiny is and whether we are staying in the Premier League or whether we are going to get relegated.
"If they do approach us, it is entirely up to Roberto whether he wants to go to Everton or stay at Wigan."