The Anfield side are seeking a manager following Wednesday's departure of Kenny Dalglish.
And Whelan told Sky Sports News: "If Liverpool are serious then I may lose him."
The Wigan chairman revealed the Reds made an approach on Thursday afternoon 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."