The Spanish head coach has kept the Latics in the Premier League over the last number of years, and led the DW Stadium side to beat Manchester United, Arsenal and Newcastle in an excellent end-of-season run-in.
Whelan would like Martinez to stay with Wigan, but will wish him well at Anfield if he does accept the position.
“He has flown into Miami so I am assuming he is in a meeting with the American owners of Liverpool,” Whelan confirmed on Sky Sports.
“I have given him permission and he is just carrying out that permission. He has to listen to what they are offering.
“I think it will depend on the attitude of the owners in America, because I don’t think the owners from America fully understand the game of football in England.
“We have to wait and see what they offer Roberto and what kind of control he has, because Roberto likes total control.
“If he doesn’t get that I don’t think he will take the job.
“Hopefully he will stay with Wigan, but if not good luck to him.
“I have asked Roberto to make his mind up as quickly as possible, and if we do lose him I will move very quickly to appoint a successor.
“I have got ideas, but hopefully he will stay with us,” he concluded.
By Gareth McKnight