The Anfield outfit have been searching for a new manager for just over a week following the shock decision to sack club legend Kenny Dalglish.
The Reds were granted permission to speak with the Spaniard soon after Dalglish departed, but as yet have been unable to do so as he is on holiday in Barbados.
John W Henry and his Fenway Sports Group colleagues are now due to hold talks with Martinez as they look to narrow down a field of candidates which initially held as many as 12 names.
Swansea boss Brendan Rodgers and Ajax manager Frank De Boer have already moved to distance themselves from the vacancy, while Marseille's Didier Deschamps and Jurgen Klopp of Borussia Dortmund have no plans to leave their current posts.
Latics chairman Dave Whelan claimed earlier on Thursday that he would set Martinez a deadline of seven days from Tuesday to make a decision as to where his future lies.
The 38-year-old has also been mentioned as a contender for the Aston Villa vacancy, but turned down the opportunity to take over at the midlands last summer to stay with Wigan.
He oversaw an impressive end to the campaign with the Latics, which included memorable victories over Manchester United, Arsenal and Liverpool to avoid relegation by seven points.
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