Comolli has been told by the board to find a new long-term manager.
He said: "Competence will be the first thing. Someone who will fit into the club philosophy and playing philosophy. Man-management is huge. Those are the three things that will be most important to the club."
Reporters asked if Dalglish met these criteria, and Comolli added: "It's honestly open to people who we think fit into what I've described. Obviously Kenny will come into this category because he has exactly what I've described.
"The answer is yes. It will be a thorough search of what we want and where we want to get to. We'll speak to Kenny about it and see where we get to."