The Latics boss met with Liverpool's principal owner John Henry in Miami on Thursday to talk about the vacant Anfield job after interrupting a family holiday in the Caribbean.
It was expected Fenway Sports Group would speak to other candidates on a short-list in the coming days but Whelan suggested developments had progressed. He did, however, say Martinez wanted to negotiate a greater degree of control of footballing issues.
"I think what he has said is, `Thank you for your offer but I only work under the following rules: I have to have complete control of football'," Whelan told Sky Sports News.
"That's normally the way in England, that's how we all work. I think they're considering his request and Roberto's considering their offer and they're going to talk again on Tuesday.
"Hopefully he stays with us but wherever he goes, he's 100% dedicated to that football club."