Martinez to hold talks with Liverpool
Wigan chairman Dave Whelan told Sky Sports: "I've always said that when a big club comes he [Martinez] will have permission to talk to them and... they don't come any bigger than Liverpool.
"I gave him permission and he'll be talking to them soon. I don't know when, but it will be quite soon."
Dalglish was sacked on Wednesday after leading Liverpool to a disappointing eighth place in the Premier League although they won the League Cup and reached the FA Cup final.
Although Wigan finished a lowly 15th they had a fine end to the season with Spaniard Martinez again showing his managerial credentials on a tight budget by rallying his struggling team.
"I would love to keep Roberto," Whelan added on Thursday.
"He is a great manager but unfortunately in this day and age of football there are two or three clubs looking for managers and I think Roberto is on the list of every one of them.
"If Liverpool are serious then we may lose him."