Fabio Capello has held talks with Liverpool and has been invited to meet with owners Fenway Sports Group.
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Roberto Martinez and Andre Villas-Boas have also held meetings with Liverpool and are on the list speak to the owners, and it is expected that they will be joined by at least one other candidate.
A source told ESPN: "The long list of candidates is now narrowing down to a workable number who are likely to go to Boston, although there is of course a chance that the owners will come over here to see the candidates."
Capello, who still has a home in West London, had ideally sought the Chelsea job, but the Blues have made no contact with the former England boss and the Italian has now ruled himself out of the Chelsea equation.
However, an agent representing Liverpool did approach Capello before the Champions League final to enquire as to his interest in the position. He has since held preliminary talks, at which he expressed a desire to be considered, and will now hold a more formal discussion.
Several coaches on Liverpool's 'long list' have ruled themselves out of the running, including Frank de Boer, Jurgen Klopp and Brendan Rodgers, while Didier Deschamps has said he expects to stay at Marseille.
Liverpool fan group Spirit of Shankly, which led the protests against former owners Tom Hicks and George Gillett, has written to Fenway Sports Group to express its concern over the way the club is being run.
"It may be that yourselves and the board of Liverpool Football Club have a vision you are working towards," SOS's letter read. "It may be that you have implemented a strategy to deliver that vision and decisions are being made to work towards this.
"However, from the outside, where supporters find themselves once again, it looks like a football club in disarray. Confusion and chaos seems to reign and no one is coming out of this with much credit, particularly the football club's image and brand.
"We need clear and pro-active communication, a confident message about the club's plans that breeds confidence amongst supporters that we are moving in the right direction. Instead, we have silence and a lack of information or understanding on decisions being made.
"As supporters we have seen all too clearly what a lack of communication from absentee owners leads to. Ultimately supporters remain in the dark once again about the plans for this football club moving forward.
"We find ourselves experiencing deja vu, where boardroom decisions lead to more questions than they answer. We ask that you speak with supporters - engage with a true representative cross section of supporters and work with supporters to provide solutions to our current problems."