The Anfield side are seeking a manager following Wednesday's departure of Kenny Dalglish.
And Whelan told Sky Sports News on Thursday: "If Liverpool are serious then I may lose him."
Whelan has always said he felt the Spaniard was destined to manage one of Europe's top clubs and he would not stand in his way should one come calling.
The Wigan chairman revealed the Reds made an approach earlier on Thursday and he gave Martinez permission to speak with them.
"When they phoned me I was actually with Roberto having a meeting on what we are doing next season," he said.
"I did promise Roberto and I have always said when a big club comes he would have permission to talk to them and 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 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."
Martinez will not be the only manager owners Fenway Sports Group speak to in their quest to replace Dalglish and he would be far from the populist choice.
Questions have already been asked about his suitability for a club the size of Liverpool, considering he only has experience at the bottom end of the Premier League with Wigan and in the Football League with Swansea prior to that.
However, his achievements at the DW Stadium - particularly this season when the Latics finished as the form side of the division with seven wins in nine matches to escape relegation once again while Liverpool were floundering - have been on a shoestring budget with players of considerably lower quality than those at Anfield.
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He is a forward-thinking manager and a great student of the game though and that has obviously gone in his favour in the first stage of the short-listing process.
Whelan has no doubts about the achievements of Martinez, who rejected an approach for Aston Villa last summer, in his three seasons at the DW.
But he knows if FSG do decide he is the man to take the club forward he will be powerless to stop the Spaniard leaving.
"I would love to keep Roberto. He's brought youngsters on and is an absolutely superb manager," he added.
"Unfortunately there are two or three clubs looking for managers and I think Roberto is on the list of every one of them.
"Managers change clubs and sometimes you don't know what's happening and you have got to accept it and get on with the job.
"I think he's going there with an open mind."
Whelan added on ESPN: "I knew that the day would come when this happened, so it wasn't unexpected.
"He is a good manager so I am not surprised a club like Liverpool want him.
"It is up to him and Liverpool now. I can imagine he will want to manage such a big club but I would willingly keep him if I could.
"He only signed a new three-year contract three months ago so I would be due compensation - but I would rather have Roberto than the compensation."
Dalglish has voiced his gratitude to Liverpool fans for their show of support following his dismissal.
In a message on Twitter, the Scot wrote: "Overwhelmed by the support of the fans. Always been special but even more so now. Thank you from the bottom of my heart. YNWA (You'll Never Walk Alone) and I never have."