Wigan chairman expects Martinez to have fresh talks with Anfield owners this week as Swansea deny receiving new approach for Brendan Rogers.
Martinez set for fresh Liverpool talks as Wigan bring forward decision deadline
The Spaniard, who met with principal owner John Henry in Miami last week while on holiday in Barbados, is due back from his break.
Latics chairman Dave Whelan has attempted to force the issue by bringing forward a deadline for Martinez to decide upon his future from next Tuesday to Thursday.
"Roberto has told me he is speaking with Liverpool again on Tuesday," he told ESPN.
"I have now made it clear that I want this sorted out by Thursday at the latest as we have to get on preparing for next season."
Indications at the weekend were that the Wigan boss was mulling over the prospect of having to work under a yet-to-be-appointed sporting director - with Dutchman Louis van Gaal strongly linked - at Anfield.
Meanwhile Swansea have denied receiving a second approach from the Anfield side for manager Brendan Rodgers following reports at the weekend suggesting FSG were eyeing the Northern Irishman as Kenny Dalglish's successor.
"We would like to clarify the speculation in the press surrounding our manager Brendan Rodgers," Swansea said in a statement.
"We would like to confirm that there has been no contact from Liverpool and nothing has changed since our previous statement on the issue."
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