Wigan chairman Dave Whelan claims manager Roberto Martinez has been made an offer by managerless Liverpool but will await a further meeting before making his decision.
The Latics boss met with Liverpool's principal owner John Henry in Miami on Thursday to talk about the vacant Anfield job after interrupting a family holiday in the Caribbean. Whelan said that Martinez - who would be expected to work under a technical director - wanted to negotiate a greater degree of control of footballing issues.
"I think what he has said is, 'Thank you for your offer but I only work under the following rules: I have to have complete control of football'," Whelan told Sky Sports News. "That's normally the way in England, that's how we all work. I think they're considering his request and Roberto's considering their offer and they're going to talk again on Tuesday."
He added: "Hopefully he stays with us but wherever he goes, he's 100% dedicated to that football club."
Liverpool have declined to comment on Whelan's claims.
It was anticipated the process of finding a replacement for Kenny Dalglish would have picked up pace next week with Henry and chairman Tom Werner likely to travel to England.
Martinez remains the favourite with the bookmakers, although that could have something to do with the fact he is the only contender publicly confirmed as being in the running.
Former Porto and Chelsea boss Andre Villas-Boas appears to have dropped out of the reckoning but it has been reported the Reds have not ruled out a second approach for Swansea's Brendan Rodgers after he declined their initial invitation to open preliminary talks.
Whelan, who set his manager a deadline of June 5 to decide his future, said on Thursday he was not convinced Martinez would take the Liverpool job because of the structure under which he would be expected to work.
Former Wigan and Liverpool goalkeeper Chris Kirkland believes the Spaniard would regret not seizing the opportunity should it arise. "What he'll be thinking to himself is: 'Will I get this opportunity again?'" said the 31-year-old, who had three seasons under Martinez at Wigan before agreeing a move to Sheffield Wednesday this week.