The Wigan manager will hold further talks with John W Henry next week after impressing the Reds’ owner during talks in Miami on Thursday and remains the leading contender to take over at Anfield.
Wigan chairman Dave Whelan has claimed that Martinez has been made a job offer but it is understood the 38-year-old has not received a formal proposal, despite increasingly appearing as the only remaining candidate for the role.
Martinez remains the clear choice of the Anfield hierarchy to replace Kenny Dalglish.
Wigan’s spectacular finish to the Premier League campaign, which saw them comfortably avoid relegation by seven points after a series of convincing victories over leading clubs, has significantly enhanced his reputation, but Fenway Sports Group has also been impressed by his skill in creating attractive teams who are able to punch above their weight.
Former Chelsea manager Andre Villas-Boas was sounded out by Liverpool and held talks in Boston, but Martinez has always been the preferred choice for the Reds as they seek a young, dynamic coach who is capable of introducing a footballing ethos which runs through all levels at the club.
Jurgen Klopp, Frank de Boer and Brendan Rodgers all ruled themselves out of contention while the likes of Pep Guardiola and Jose Mourinho were not considered realistic targets. The desire for a young, progressive manager has ruled Fabio Capello, Rafael Benitez and Harry Redknapp out of contention.
Whelan suggested in an interview on Friday that Martinez has been made an offer by the Reds, adding that the Latics boss would wants "full control" of football matters if he is to take over at Anfield.
"He went yesterday to Miami and had a very constructive meeting with the owner of Liverpool," Whelan told Sky Sports News. "They're going to talk again on Tuesday. They've made Roberto an offer and he has agreed to consider it. "He is also aware that I have said 'I'd love to keep you but I need a decision by Wednesday or Thursday of next week'. "In the meeting I think they've made him an offer and he's said 'what are my responsibilities'. "These are American owners and the rules and regulations are a bit different from what we English set down. "Roberto is a seven days a week, 12 hours a day worker and I don't know whether they realise how hard he works. "He has rules and regulations to be fully in charge of football and I know he won't move anywhere unless he is fully in charge of the football. "I think he's considering it and I think he'll give it fair consideration."