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 were 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."
Dalglish, speaking to journalists at Anfield on Monday for the first time since he was appointed, insisted he is happy with his current caretaker role and denied seeking any assurances for his long-term future when he was offered the job by Liverpool co-owner John Henry.
"My understanding is that it's until the end of the season and that's no problem for me," said Dalglish, whose first match in charge ended in a 1-0 FA Cup third-round defeat to arch rivals Manchester United on Sunday.
"I've heard stories about demanding this and demanding that, but when I was phoned on Saturday morning and asked if I'd take the job it was a straightforward 'yes' and that was it for me.
"There's no conditions, no promises, there's nothing. I came back to work at a club that myself and my family are eternally grateful for many things they have done for us and when I was asked to do it there was no way I was going to be disrespectful and say 'no'.
"I am here to be of help to the club and if that means Kenny Dalglish is not the manager that is not a problem.
"If at the end of the season the owners have their eyes on someone else then I have no problem stepping aside because if I didn't I wouldn't be true to my word.
"I would do it readily if it meant the club improving."
Liverpool will resume their stuttering Premier League campaign at Blackpool on Wednesday.
And Dalglish joked that in the current climate he may be fortunate to see out the season with the Reds.
"If I can get to the end of the season then I'll probably end up as one of the longest-serving managers in the Premier League any way," he said.
Comolli, who has previously worked for Arsenal and Tottenham, was appointed by new owners New England Sports Ventures (NESV) in November to help the club identify potential transfer targets.
But the Frenchman insisted Dalglish would have the final say on all new signings.
"As I have always said, if Kenny is not happy with a player we think could make the team better, or if he thinks it is not the right timing, it will always be down to the manager to say he is not happy."
Dalglish said he has not had time to think about transfer targets yet.
"I am sure the owners have an opinion about the football club, they own it so they are entitled to, but that is why they put Damien in his position and me in mine," he said.
"They will leave it in our hands as to whether we need players or not."