The 38-year-old, who has led Wigan Athletic to Premier League safety for three years running, has been given permission to speak to Fenway Sports Group about the vacancy by Latics owner Dave Whelan.
Martínez is reported to be Henry’s preferred choice to transform the Reds’ ailing fortunes and help guide the Merseyside outfit back into the Champions League again.
Liverpool will be keen to avoid another rejection after Brendan Rodgers, Jurgen Klopp and most recently Frank De Boer all declined the chance to discuss the Anfield vacancy with the club’s owners.
“I am honoured by the request, but I am only just getting started with Ajax,” De Boer told De Telegraaf on Monday.
“In Amsterdam we are on a new path and, along with the club and Wim Jonk and Dennis Bergkamp, my colleagues in the technical heart, I want to bring good things. That’s why I will stay loyal to Ajax in the coming years.”
Meanwhile, a statement from Swansea ruled Rodgers out of contention last week: “The club is pleased to confirm that Brendan has declined the opportunity to speak about the vacant position.”
Former Chelsea manager André Villas-Boas is believed to be Martínez’s closest rival to replace Dalglish at Liverpool.
But Wigan owner Whelan has issued his backing for the Spaniard. “I think he’s wonderful, the best manager I have ever worked with,” Whelan told the BBC last week.
“I was working with Roberto when I got the message. I told him there and then and asked if he wanted to speak to Liverpool and he said ‘yes’.
“I’ve always said a big club will come for him and I will release him immediately.”
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