Wigan owner Dave Whelan says Roberto Martinez is meeting with Liverpool’s owners in Miami.
Whelan gave Martinez permission to speak to the Reds last week and has given his manager a deadline of 5 June to resolve his future.
“Roberto is in Miami today and you can only assume what he’s gone there for [to talk to the Liverpool owners],” Whelan told BBC Sport.
“He is honest and up front and I expect to hear from him in the next 48 hours.”
Martinez’s negotiations mark the formal start of Liverpool’s interview process for their managerial vacancy, created when Kenny Dalglish was sacked on 16 May.
Swansea manager Brendan Rodgers and Ajax’s Frank de Boer 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.
Former Swansea boss Martinez, 38, who rejected the chance to join Aston Villa last summer, is scheduled to return from a holiday in Barbados next Tuesday and has been given a seven-day deadline by Whelan.
Whelan is hoping the situation is resolved quickly.
He added: “He is out in the Caribbean so it’s only two hours to Miami from there.
“If he decides to go, which I hope he doesn’t, I’ve got to replace him as soon as possible.”