The 38-year-old has been locked in talks with Reds owner John W. Henry this week and the pair were spotted in Miami together on Thursday fuelling speculation that his appointment was imminent.
More discussions are being planned for Tuesday when it’s expected that the Spaniard will be announced as the replacement for Dalglish who was sacked nine days ago.
Latic’s chairman Dave Whelan set Martinez a deadline of June 5th to decide over his future at the DW Stadium but now claims he has been offered the job.
It’s expected that the former Swansea boss will work under a technical director, rumoured to be Louis Van Gaal, and Whelan believes he won’t sign until he’s certain he has full jurisdiction of football matters.
“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'” he 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 per cent dedicated to that football club.”
It was thought that Fenway Sports Group would continue to speak to other candidates they wanted fill the shoes of Dalglish with Andre Villas-Boas reportedly on their radar.
The former Chelsea boss has now dropped out of the reckoning as has Swansea manager Brendan Rodgers who was the early frontrunner for the role.
Henry and chairman Tom Werner will fly to England next week to conclude their talks with bookmakers favourite Martinez before handing him the Anfield reins.