Wigan chairman Dave Whelan expects manager Roberto Martinez to stay at the DW Stadium and help the relegated FA Cup winners challenge for promotion next season.
Martinez, who was offered the Aston Villa job in 2011 and was interviewed by Liverpool last summer, is the favourite to succeed David Moyes at Everton after helping Wigan win the first major trophy in their 81-year history at Wembley on Saturday.
But Athletic's eight-year stay in the Premier League came to an end when Tuesday's 4-1 defeat at Arsenal sealed their demotion to the Championship.
Owner Whelan told Talksport: "We've got one ambition now, and that is to come straight back up next season. We will fight next year, and we'll look to come back within that first season - it's so important."
Whelan and Martinez have had a close relationship since the 76-year-old brought the young Spaniard to Wigan in 1995 and he appointed him manager in 2009.
The millionaire businessman reiterated that the 39-year-old will be allowed to leave if he wants to but believes that the former Swansea manager is likely to remain at the club.
He added: "Roberto knows how I feel about him and I know how Roberto feels about me and the club. He's a very, very loyal gentleman.
"When the day dawns - and it will - when he says, 'chairman, I want to go to this or that club', I will release him immediately.
"He is aware of that, and if that time is now, so be it. But somehow I don't think it will be. I'm just hoping Roberto waits and has another one or two years with us, because he will eventually go to a top European club."
Whelan said Everton are yet to contact them about Martinez, explaining: "The club have heard nothing whatsoever. Everton are a super club and they know the rules and regulations. They are very mannerly and I don't think they would ever approach Roberto before the season is over."
Neil Lennon, Malky Mackay, Michael Laudrup, Vitor Pereira and Phil Neville have also been linked with the vacancy at Goodison Park.