The 38-year-old Latics manager was pictured with Liverpool owner John Henry on Thursday after Martínez flew to Miami from Barbados, where he was on holiday, for talks about the vacant position.
Whelan, who brought Martínez to Wigan from Swansea City in 2009, has set next Thursday as the deadline for the Spaniard’s future to be resolved, with the 75-year-old revealing his manager will speak with the Reds again next Tuesday.
“He had a meeting on Thursday with the owner of Liverpool in Miami,” Whelan told BBC Sport. “I think they have made some kind of offer.
“They will speak again on Tuesday. I’ve said I want a decision by Thursday.
“We are having a meeting on Tuesday when he’s going to put everything to me. He’s very honest. He arrives back in the morning and we will get together in the afternoon.”
Whelan also revealed that Martínez wants assurances from the Liverpool owners Fenway Sports Group that he will have sufficient control to implement the changes needed at the club.
“I think Roberto has put his cards on the table and said ‘If I’m going to Liverpool I want the following’,” added the Wigan owner.
“Roberto has to run the football club from top to bottom. Without that I don’t think he would go.
“I should not be saying how good Roberto is because I want to keep him. There’s no question he’s the best young manager in Europe.”
Liverpool are yet to comment on Whelan’s claims.
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