Liverpool will continue the process of sounding out prospective candidates for the vacant manager's job this week.
Another name was definitively removed from the list after Ajax coach Frank de Boer turned down the chance to discuss the position, while Marseille coach Didier Deschamps has said he expects to be in charge of the Ligue 1 club for the start of pre-season training.
Swansea's Brendan Rodgers and Borussia Dortmund's Jurgen Klopp have already stated their intentions to remain with their clubs next season.
But such is the breadth of talent owners Fenway Sports Group are keen to assess there is no sense currently that options are becoming limited.
Principal owner John Henry and chairman Tom Werner opted for a recruitment process which involved sounding out the best possible candidates, irrespective of how numerous that list may have been, and they are sticking to that blueprint.
It is understood by next week they could be in a position to draw up a proper shortlist of possibly up to five contenders.
But the Americans, assisted by managing director Ian Ayre, are determined to thoroughly examine all avenues to ensure they give themselves the best chance of finding the right man to succeed Kenny Dalglish, who was sacked almost a week ago.
De Boer turned down the chance to speak to Liverpool as he feels he has an unfinished job at his current club, despite winning back-to-back league titles having taken over from Martin Jol in 2010.
"I am honoured by the request but I have only just started with Ajax," the 42-year-old former Holland international told Dutch newspaper De Telegraaf.
"In Amsterdam, we are on a new path and I, along with Wim Jonk and Dennis Bergkamp - my colleagues on the technical side - want to bring success.
"That's why I will stay loyal to Ajax in the coming years."
Deschamps, having been considered for the job after Rafael Benitez's departure almost two years ago, was also believed to be one of the people FSG were keen to talk to.
Marseille finished a disappointing 10th in Ligue 1 but the former France international believes his future remains at the Stade Velodrome.
"It is expected that I be there next season," he told French journalists.
"When it goes badly, there is need to recharge. I will leave on vacation but it is expected that I be there (Marseille) for July 2."
Former Porto and Chelsea manager Andre Villas-Boas remains one of the favourites while Wigan's Roberto Martinez has also been given permission to speak with Henry and Werner.