Chairman Dave Whelan does not believe Roberto Martinez should leave Wigan for Everton as they are not a big enough club for the Spaniard.
The Latics were relegated to the npower Championship following a 4-1 defeat to Arsenal which further increased speculation that Martinez is set to leave the DW Stadium.
The 39-year-old has emerged as one of the bookmakers' favourites to replace David Moyes at Goodison Park but Whelan told Sky Sports News: "Roberto, when he goes to a big club, I was thinking one of the big European clubs or a big English club."
He added: "Everton are a great club by the way and, if he chose to go to Everton, I'm sure the Everton supporters would be delighted.
"I have nothing whatsoever against Everton, I love that club. I love playing against them, I love the supporters, everything about them is top class and if he went to Everton I would wish him the very very best of luck.
"But I just think he will go to a bigger club than Everton, in reality.
"Throughout Europe there are some massive clubs and Roberto being what he is, he is so good.
"Sooner or later, I've always said he will go to a massive European club and he'll do well. Whoever he goes to, Roberto is a brilliant, brilliant manager."
Despite the talk of Martinez's bright future on the bigger stage, Whelan insists his exit is not a foregone conclusion this summer.
"I will have a meeting with Roberto on Monday next week and, as every year and every week, we sit down and have a meeting," he said. "We both trust each other implicitly and whatever Roberto says I believe and I know whatever I say to him, he will believe that."