The Latics beat Manchester City 1-0 on Saturday to win the FA Cup, but are four points from safety with just one game in hand and could drop out of the Premier League after surviving three successive relegation battles under Martinez.
Their former Swansea boss has been linked with a switch to Merseyside to replace the outgoing manager David Moyes who was named Sir Alex Ferguson’s successor at Manchester United, but the owner believed that he would stay despite being allowed to leave.
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"It’s Roberto’s decision. All I do is support him. If he comes to me and says ‘I want to go to whichever club’ I’ll say ‘okay’ and release him immediately because we have such a great working relationship."
Martinez arrived at the DW Stadium in 2009 to manage the club at which he spent five seasons as a player, and went on to decline an offer from Aston Villa in 2011 and Whelan went on to praise him for his integrity over the period.
He continued: "Roberto is always in demand. But he deals with it. He tells me everything and he’s the most honest man you’ll ever meet.
"If anybody approaches him he comes to me and says such a club has approached me.
"I don’t think he’ll go this season, but if he does I’ll shake his hand and wish him good luck because he’s been a brilliant manager for us."
Commenting on Saturday’s win over City courtesy of Ben Watson’s late header from a corner, he added: "The dream for a football club like Wigan, to come from the Lancashire Combination only 24 years ago and win the FA Cup, is a remarkable achievement.
"Our supporters were in ecstasy out there. They just couldn’t believe it but we deserved it. I thought we played Manchester City off the park."