The pair met on Thursday, with plans for the club's training facilities and youth development policy emerging as key factors in whether the Spaniard stays with the club following their relegation from the Premier League.
"I've had a good meeting with Roberto, very constructive. He's asked me certain questions about training facilities and development of our youth players, and generally on what progress Wigan can make," Whelan told Sky Sports News.
"It was very encouraging, but I don't want to promise Roberto certain things that I cannot deliver.
"We have had very good news on our application for planning, so I'll be able to tell Roberto on what I can and cannot do in terms of what he is asking.
"He wants to build Wigan Athletic, and I want to build Wigan Athletic. We want to get back in the Premier League and we want to do all kinds of things at our football club.
"We are both mad, mad keen to do that but I cannot promise Roberto things I cannot deliver on. I've asked if I can speak to him again on Monday so the ball is back in my court.
"It's nothing to do with money or contracts. The good part of it is Roberto, as usual, is up front. He's only interested in developing Wigan Athletic."
Martinez has been strongly linked with vacant managerial positions at Everton and Stoke, and Whelan admits that what he says in his next meeting with the man he brought to the club as a player in 1995 will be crucial.
"The ball's in my court, I've got to say to Roberto 'I'm going to deliver on the following things', and it's mainly training ground facilities and youth development.
"We've gone a long way on the path and he wants to complete it. I agree with him entirely but I want until Monday to think about it."