Martinez flew to Miami after holidaying in Barbados to meet Liverpool's principle owner John Henry and, according to Whelan, is set for a second meeting on Tuesday.
"He had a very constructive meeting. They made an offer and he has agreed to consider it," Whelan said on Sky Sports.
"I am still not convinced it is a foregone conclusion, because they put their points on the table and Roberto put his," Whelan also told ESPN.
"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.
"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."
