New Liverpool caretaker manager Kenny Dalglish will be a candidate for the post on a permanent basis.
The Scot is in charge until the end of the season, with director of football Damien Comolli tasked with finding Roy Hodgson's long-term successor.
Asked whether former Reds player and manager Dalglish would be considered Comolli said: "The answer is yes."
Dalglish added: "If I do really well and someone better than me comes along I will have no problem whatsoever."
Dalglish, who won eight league titles as a player and a manager with Liverpool between 1977 and 1991, applied for the job in the summer after the departure of Rafael Benitez, only to be overlooked in favour of Hodgson.
But when a dismal run of results brought a premature end to Hodgson's reign on Saturday the club turned to the Anfield legend to take charge until the end of the season.
That gives Dalglish a chance to stake his claim for the long-term job while Comolli scours the globe for a viable alternative.
Asked what the criteria was for identifying the next permanent manager, Comolli said: "Competence, someone who will fit into the club and playing philosophy and huge on man-management - the three things most important to the club.
"It is open to people that we think fit into what I have described and Kenny obviously fits into that category.
"There will be a thorough search of what we want to do, where we want to get to and we will talk to Kenny about it and see where it takes us."
More to follow.
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