Wigan owner Dave Whelan believes Roberto Martinez has been made an offer by Liverpool to take over as manager.
Martinez broke off from his holiday in Barbados for talks with the Reds and Whelan says he now wants his manager's future resolved by next Thursday.
"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."
Liverpool have declined to comment on Whelan's claims.
Martinez received permission to speak to the Reds last week and was previously handed a deadline to sort his future of 5 June by Whelan, which the Latics owner now appears to have brought forward.
The Spaniard, who met with Liverpool's American owners Fenway Sports Group in the United States, returns from his holiday on Tuesday.
Whelan revealed: "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."
However, Whelan insisted it is by no means certain the 38-year-old will accept the offer to take over at Anfield.
"I think Roberto has put his cards on the table and said 'If I'm going to Liverpool I want the following'," said 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."
Asked about the prospect of Martinez taking over at Liverpool, Reds skipper Steven Gerrard said: "We'll have to wait and see. It's news for me. I am aware Roberto Martinez has been speaking to the club. If he is the manager he has my support."
Ajax manager Frank de Boer and Swansea's Brendan Rodgers have turned down the chance to speak to the Anfield club.
Former Chelsea boss Andre Villas-Boas is among a host of other potential candidates that have been linked with the vacancy.