The Spaniard has been linked with a number of clubs in recent weeks and the Latics' relegation from the Premier League - despite also winning the FA Cup - has led to increased speculation about his future.
Whelan said Thursday was 'D-day' for Martinez, but he remained hopeful that not only would the 39-year-old stay, but also agree a contract extension. "We have had a constructive meeting today and Roberto wants 24 hours to speak to his wife and decide what he wants to do," he said.
"He needs a bit of time, which I think is fair, and tomorrow we will know - it is decision day."
Martinez, who has 12 months left on his existing contract, has been one of the front-runners for the vacant Everton job following David Moyes' move to Manchester United.
However, Tony Pulis' departure from Stoke on Tuesday would give him another Premier League option while confirmation Manuel Pellegrini and his coaching staff are leaving Malaga could raise the possibility of him returning to his homeland.
But there is also a chance Martinez, who has previously turned down Aston Villa and was on Liverpool's short-list to succeed Kenny Dalglish last summer, will remain at the DW Stadium and try to get the club back into the Premier League at the first attempt.
"I told him exactly as I saw it: his future for the next two years lies with Wigan Athletic," added Whelan. "If he wants to opt out of his contract and go then there is a bit of compensation to be paid but I hope that won't be the case.
"I hope he will extend his contract. As I see it there are two (Premier League) clubs available and does each club want him?
"We are talking about Roberto for the whole of Europe. I am not sure which club or the other has approached him but I am sure the club which will approach him will be bigger than Wigan. I hope he stays but tomorrow I will be able to tell you."
- Sports & Recreation
- Premier League