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.
The Wigan manager has won plaudits for keeping the modest north-west side in the Premier League for the last three seasons and for playing an open, expansive brand of passing football.
The Spaniard is odds-on favourite to succeed Dalglish in the Anfield hotseat after the Scot was sacked following a lacklustre Premier League campaign where they finished eighth. A League Cup triumph and FA Cup final appearance did not spare him.
Whelan questioned whether his manager would accept the job should he be asked to work under a sporting director and not have full control at the club.
Liverpool sacked director of football Damien Comolli in April and former Bayern Munich and Barcelona coach Louis van Gaal has been linked by British media with the vacant position.
"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."
It is expected other candidates will now also be spoken to in a more formal capacity, with Henry and chairman Tom Werner likely to travel to England as FSG go about whittling down their options.
Martinez remains the favourite with the bookmakers, although that could have something to do with the fact he is the only contender publicly confirmed as being in the running.
But having spent just over a week assessing potential candidates FSG are ready to press ahead with the serious business of identifying the man they want to lead their bid to restore former glories at Anfield.
While ex-Porto and Chelsea boss Andre Villas-Boas appears to have dropped out of the reckoning it is reported the Reds have not ruled out a second approach for Swansea's Brendan Rodgers after he declined their initial invitation to open preliminary talks.