Whelan said the experiences of two of the Premier League's relegated sides - Portsmouth going into administration and Hull running up a £35million-plus debt - was a warning to all clubs to keep a firm grip on spending.
And Martinez will have to decide where he wants to save money within the current squad before he can bring in replacements.
Paul Scharner has already confirmed his departure after running down his contract while fellow midfielder Jason Koumas, one of the club's bigger earners, is also set to leave after his deal expired.
Captain Mario Melchiot is also out of contract and could be another to leave as Martinez looks to freshen up his squad, having already agreed the free transfer of Paraguay and Club Brugge centre-back Antolin Alcaraz.
"First of all we have to decide who is going out before we can decide who is coming in," Whelan told the Wigan Reporter.
"But Roberto has to accept - like every other manager in the Premier League - that there has to be a limit on what they can do.
"I think that has been reinforced by what's happened at Portsmouth and the trouble that Hull are in.
"Everybody in the Premier League has to be looking to try to break even.
"I'll be meeting with him this week to have a chat about the situation, and we'll see how we go."
Martinez's other issue is trying to hang on to his better players, with player of the year Charles N'Zogbia already attracting interest from Birmingham.
The Latics boss has previously said he does not have to sell but admitted if a bigger club came in for any of his players they would have to consider what was best - a sentiment previously echoed by Whelan.
Back in March the chairman admitted: "I think this current team has two or three players - Hugo Rodallega and Charles N'Zogbia, for example - who can go on to play for top clubs and I would never stand in the way of those players should that opportunity arise."
Whether Birmingham fall into the "top club" category is doubtful and, in any case, a reported £8million bid from the Blues falls well below Wigan's valuation.
Having bought the Frenchman for £6million 15 months ago Wigan feel he has enhanced his reputation, particularly this season.
Last summer the Latics sold winger Antonio Valencia to Manchester United for £16million after buying him for a fraction of that amount 18 months previously and they are not prepared to allow N'Zogbia to leave without making a significant profit.