Martinez is now expected to fly to Boston early next week to meet John Henry and Tom Werner.
Latics chairman Whelan, talking to The Times on Thursday, said: "It is true that I've given Liverpool permission to speak to Roberto.
"I don't know the exact timescales of when he is due to meet with the Liverpool owners, but I will never stand in Roberto's way."
FSG are expected to have other managerial targets in mind as well as they seek a replacement for Kenny Dalglish.
Whelan later elaborated to Sky Sports News: "When they (Liverpool) phoned me, I was actually with Roberto and having a meeting about what to do next season.
"I have always said that when a big club comes, he will have permission to talk to them - and Liverpool, they don't come any bigger than Liverpool.
"I gave him permission and he will be talking to them soon. I don't know when, but it will be quite soon.
"When Liverpool sacked Kenny, I have to say I thought Liverpool would be knocking on the door and sure enough they are.
"I would love to keep him, but I have told Roberto he has my permission to speak with Liverpool."
Reds talks for Martinez - Whelan | News
Hope it's not true.