Wigan's relegation was confirmed by their 4-1 loss to Arsenal on Tuesday night, fuelling speculation that Martinez and a number of players will be on their way out of the club this summer.
Whelan has also spoken previously about his plans to pass the club on to his grandson, but he is committed to staying on as chairman now Wigan have gone down as he wants to see them win promotion back to the top flight.
"I have one ambition left in my life, and that is to get Wigan back in the Premier League," he told Sky Sports News.
"When we got to the Premier League we were supposedly going to go back down the next year, so to stay in eight years is a great achievement and we want to be back in a year's time."
Whelan admitted that he always feared for Wigan's chances of staying up after they were beaten 3-2 at home by Swansea City.
"The loss to Swansea was the decisive moment," he said. "I never thought we could go to Arsenal and get three points. That was a tough call.
"It is painful when you get relegated out any division, let alone the Premier League, but we have got one ambition in mind and that is to bounce back next season.
"It is difficult because the Championship is a very tough league and we will have over 50 games to play next season, but we'll be up for it."
Wigan face extra games next season after winning the FA Cup on Saturday, and Whelan confirmed their victory parade would take place next Monday.
Whether the occasion will mark a farewell for Martinez remains to be seen, as the Spaniard continues to be linked with a move to Everton to replace David Moyes.
Whelan has a great relationship with Martinez and will not stop his manager from leaving when he thinks the time is right, but he suspects he may stay for now before eventually going to a club even bigger than Everton.
"I will have a meeting with Roberto next week and we both trust each other implicitly," said Whelan. "Roberto has been a fantastic manager for Wigan and I hope he will continue to be a fantastic manager for Wigan for at least two or three years to come.
"I have always said that if he wants to leave he can just say so and I will release him immediately.
"I just think that Roberto, when he goes to a big club, that I was thinking of a big European club.
"Everton are a great club by the way and if he chose to go to Everton I am sure their supporters would be delighted.
"Personally I have nothing against Everton. I love that club. Everything about them is top class and if he went there I would wish him the best of luck, but I just think he will go to a bigger club than Everton."
Whelan does accept there will be changes to the Wigan squad at the end of the season and a number of their best players could leave to join other clubs.
He said: "Some of the players who want to stay in the Premier League will definitely want to move. I can't blame them for that, so if the players come and say they want to go, and we get the right offer, I will not stand in their way.
"We have got to be fair to the players, and they have got to be fair to us."