The FA Cup-winning boss is reported to be the Toffees' top target after David Moyes agreed to join Manchester United this summer.
The Latics chief does not expect counterpart Bill Kenwright to broach the subject of the Spaniard until after the relegation-threatened side's Premier League future is decided but admits that the the former Swansea City manager could be tempted by Goodison Park.
"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 favorite 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."