Dalglish has been appointed caretaker manager for the rest of the campaign but at the press conference to introduce the King to the press yesterday, Damien Comolli admitted he could keep the job if successful.
"Competence, someone who will fit into the club and playing philosophy and huge on man-management. That will be the three things most important to the club," said the Reds' Director of Football.
"It is open to people that we think fit into what I have described and Kenny will come into that category.
"There will be a thorough search of what we want to do, where we want to get to and we will speak to Kenny about it and we'll see where it takes us."