Discussions will be held following the Latics' final game of the season against Aston Villa on Sunday.
"We'd all love him to stay," Whelan told BBC Radio 5Live. "At the end of the season what we always do is get together and have a talk.
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Martinez, who guided Wigan to their first FA Cup triumph in their 81-year history on Saturday, has been linked to the vacant Everton position after David Moyes’ departure to Manchester United.
But in spite of this, Whelan insists that he will not be resigned to parting ways with his manager, having fended off interest from high-profile clubs such as Liverpool and Aston Villa in recent seasons.
"He's being chased regularly by some very, very big and wealthy clubs around England," he said. "We'll have talks to persuade him; if we need to persuade him because he is a dedicated man.
"He goes by his word. He's so honest and we respect him enormously. Everybody in Wigan hopes that Roberto stays with us."
After defying the odds with an eight-year stint in the top-flight, Wigan’s 4-1 loss to Arsenal on Tuesday finally confirmed relegation for the Latics, but Whelan admits that he suspected the worst after Wigan’s dismal 3-2 home defeat to Swansea last week.
"The writing was on the wall when we lost to Swansea at home,” he said. "We should have won that match, but it's football. We've got to fight our way back next season."
And despite what the future may hold, Whelan is adamant the club has much to proud of as they target an immediate return to the top flight next season.
"To have eight years at this level is incredible," he continued. "We have beaten every top club and financially we are in a strong position. As a Wigan fan, it is a time to be proud of what we have achieved.
"The FA Cup is an achievement we will never lose as a club. It is our first silverware, but it is a real shame it happens in the same season as relegation.
"You don't normally get teams good enough to win the cup going down - that is why it is difficult to take.
"When you walk into the dressing room after this match, it is heartbreaking."