The Latics' 4-1 defeat at Arsenal confirmed their relegation to the Championship, just three days after they lifted the FA Cup.
Martinez has been linked with the soon-to-be vacant manager's job at Everton but Whelan reckons he will remain at the DW Stadium.
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.
"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 added that there had been no contact from Everton.
"The club have heard nothing whatsoever," he said. "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."