Martinez in Miami to talk to Liverpool
"Roberto is in Miami today and you can only assume what he's gone there for," Whelan told the BBC.
"He is honest and up front and I expect to hear from him in the next 48 hours.
"If he decides to go, which I hope he doesn't, I've got to replace him as soon as possible."
The 38-year-old Martinez, who kept Wigan in the Premier League with a late surge up the table, could succeed Kenny Dalglish who was sacked by Liverpool last week after a disappointing season in which they finished eighth.