While Brendan Rodgers and Frank De Boer decided to stay with Swansea and Ajax respectively, Martinez is set to fly to Boston this week to have a second interview for the job with Liverpool's principal owner John Henry, according to the Daily Mirror.
The paper says that the Spaniard is Henry's "preferred choice" for the job even though he is not the top pick with many of the fans.
"Henry is keen to assess Martinez in person and feels he ticks all the right boxes to become the Reds’ next boss," says the Mirror.
"The American is pressing ahead with Martinez, even though the Spaniard has little support among fans who want to see
However, the paper also notes that: "Despite Martinez’s talks with Liverpool, he is not guaranteed to get the job and the Reds still have other names on their shortlist but he will be the first one to be seen personally by Henry.
"Liverpool bosses would like to speak to
Another name that is cropping up as a potential contender in more and more newspaper reports is former England boss
The Daily Telegraph says that "the possibility of trying to employ Capello is being discussed with increased seriousness" at Anfield.
It says there might be interest from the Italian too, noting that: "While Capello’s preference would be to work in London, he would give serious consideration should Liverpool make an approach.
"However, he would also be very expensive and although Liverpool are unlikely to want to match his wage demands, and the scale of transfer budget he would require, talks could still take place in the hope of persuading him to accept the job on a shorter-term, two-year contract."
Another manager that could be available soon is
The Times runs a similar tale of doubt on the part of the Russian owner, but says that he may still offer Di Matteo a one-year contract - a trial for the permanent job.
Let's move away from manager talk and round up the transfer rumours for you.
Meanwhile Tottenham have been handed a huge boost after top target