ESPN has been told Roberto Martinez wants assurances over the level of control he will have over team affairs before agreeing to become Liverpool's new manager.
Wigan boss Martinez flew to Miami to hold talks with Liverpool's owners FSG this week as the Reds upped the ante in their search for a successor to the sacked Kenny Dalglish.
Latics chairman Dave Whelan has recently warned Martinez that he may not have full control of the club's transfer dealings, believing FSG wish to adopt a more European-style recruitment structure.
Speaking on Friday, Whelan confirmed Martinez's first set of talks with FSG have now come to a conclusion, with further discussions planned next week as the Spanish coach mulls over whether the position at Anfield is right for him.
Whelan told ESPN: "Roberto has had a constructive meeting with Liverpool. He is now back at my home in Barbados. He returns to London on Tuesday, when he will have further talks with Liverpool and when a decision will be made.
"There was no other manager mentioned so I imagine they want Roberto. I don't want to lose him, but I made him a promise when he first joined that, if a big club came in for him, I'd let him go, and I will honour that promise.
"I am still not convinced it is a foregone conclusion, because they put their points on the table, and Roberto put his. He listened to their points, but I think they also listened to his and I think they are coming to terms with the way English football is run. Roberto wants control over football matters and that includes transfers, and if they agree to that, then I can see him becoming the Liverpool manager.
"Roberto works seven days a week, sometimes 12 hours a day. He is not the average manager, but he likes to run the football side, and I can see Liverpool's point of view about the amount of money spent on players. If they agree to let Roberto take responsibility for the transfers than I think he will go there, and I can see that Liverpool have set their sights on him."
Later, talking to Sky Sports, Whelan added: "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. 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.''