The Spaniard is currently on a holiday in the Caribbean but took a short flight to Miami where he met FSG officials.
Martinez’s current employer Whelan revealed the trip after talks with his manager.
‘I got a phone call this morning and Roberto was on his way to America, he’s flying down to Miami and is meeting Liverpool now,’ he said.
‘I didn’t ask him what he has decided to do but I told him I wanted it sorted out sooner rather than later.’
Whelan added: ‘He has to listen to what they are offering. He is just doing what I gave him permission to do.’
Martinez has emerged as a front-runner after reports that former Chelsea manager Andre Villas-Boas is out of the reckoning.
But the Latics chairman warned Martinez may reject Liverpool if they don’t meet his demands.
He told Sky Sports.: ‘A little bit will have to do with the attitude of the owners because I don’t think they fully understand the game of football in England.
‘Roberto likes total control, from the youngsters at 16 to the first team.
‘If he doesn’t get that I don’t think he will take the job.’
FSG has spent the last week, since sacking Kenny Dalglish, sourcing a replacement.
It is part of the strategy it has to reorganise the structure at Anfield which will see the appointment of a technical director above the manager.
That approach has been questioned by Whelan, who added: ‘My understanding is that Liverpool are seeking a final shortlist of six managers whom the owners would like to interview.
‘I am amazed that they think they can do that, it sounds very much an American way of dealing with these issues in sport, but I would wonder how those six managers might feel.’