Dalglish was sacked on Wednesday afternoon following a disappointing season in charge at Anfield which saw Liverpool limp to an eighth-place finish.
Martínez, who turned down an approach from Aston Villa last summer, is one of a number of candidates on Fenway Sports Group’s shortlist to succeed Dalglish.
“Liverpool rang us and asked for permission to speak to Roberto, which I’ve given,” Whelan told BBC Sport.
“I’d love to keep him but if he wants to move to Liverpool I will have to say good luck.
“When Liverpool sacked Kenny Dalglish I thought they would be looking around and they say they want a young, ambitious manager. You can’t get one better than Roberto, so I expected them to call.”
Martínez joined Wigan from Swansea City in 2009 and the 38-year-old has managed to keep the Latics in the top flight for three successive seasons.
“I think he’s wonderful, the best manager I have ever worked with,” added Whelan.
“I was working with Roberto when I got the message. I told him there and then and asked if he wanted to speak to Liverpool and he said ‘yes’.
“I’ve always said a big club will come for him and I will release him immediately.”
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news