Wigan chairman Dave Whelan on Friday claimed Latics boss Roberto Martinez is weighing up an offer from Liverpool to take over as manager of the Anfield club.
Martinez left a family holiday in the Caribbean to meet Liverpool owner John Henry in Miami on Thursday and Whelan said the Spaniard was offered the chance to succeed Kenny Dalglish, who was sacked after a disappointing Premier League campaign.
But Martinez is not sure whether to accept the terms, as it would involve working under a technical director, with one candidate believed to be former Ajax coach Louis van Gaal.
Instead, the 38-year-old would prefer a greater degree of control over transfers and other footballing issues, according to Whelan.
"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.
"Hopefully he stays with us but wherever he goes, he's 100 percent dedicated to that football club."
Whelan, who set his manager a deadline of June 5 to decide his future, said earlier this week that he was not convinced Martinez would take the Liverpool job because of the structure under which he would be expected to work.
Liverpool have declined to comment on Whelan's claims but Martinez, whose stock has risen since he masterminded Wigan's late-season climb away from the Premier League relegation zone, remains the favourite with the bookmakers.
Former Porto and Chelsea boss Andre Villas-Boas appears to have dropped out of the reckoning, while the Reds have reportedly not ruled out a second approach for Swansea's Brendan Rodgers after he declined their initial invitation to open talks.