The Latics chief revealed on Thursday that the Spaniard had taken a break from a family holiday in the Caribbean to meet top executives from Fenway Sports Group in Miami. There are still other candidates to consider as FSG were hopeful of drawing up a shortlist of up to five people to interview next week.
But Whelan believes the new structure being implemented at Anfield, with a yet-to-be-appointed technical director overseeing general football matters, would not be appealing to Martinez, and he told Sky Sports: "A little bit will have to do with the attitude of the owners because I don't think they fully understand the game of football in England."
He went on: "Roberto likes total control, from the youngsters at 16 to the first team. If he doesn't get that I don't think he will take the job."
Whelan added on ESPN: "My information is that the new Liverpool manager will not be given full responsibility of the football department.
"The set-up on the football side goes well beyond the norm even with a director of football. There will be somebody else signing players and they might not necessarily be the choice of the manager.
"My advice to Roberto is to think very carefully about this, but Liverpool are a big club and I hope that they remain one of the big clubs.
"I've asked Roberto to make his mind up as soon as possible. If we have to lose him I will move very quickly to appoint a successor as I have ideas. Hopefully he will stay with us but we will wait and see.
"He has not said anything to me yet about what he plans to do but I have told him what I think about it, of course I have.
"I have told him it doesn't feel right what is happening at Liverpool, but its for him to make his own mind up. If it's yes to Liverpool I will accept it and get on with life. But if it's no I'll be delighted. I hope he will stay but I told him I need an answer in the next seven days."