The Hoops boss is being linked to the Foxes, who are thinking about sacking manager Brendan Rodgers.
However, Leicester find themselves bottom of the Premier League, and Dalglish does not think Postecoglou will be eager to leave a potentially title-winning team for a relegation fight.
"Ange has been at the centre of some speculation, due to the excellent job he has been doing at Celtic," Dalglish wrote in the Sunday Post.
"Now he is still being mentioned in England as a contender for the Leicester City job, should there be a parting of the ways with Brendan Rodgers. For me, though, that is a non-starter. Why would Ange want to leave Celtic to go there? Why would he leave a Champions League club for a team that may well end up fighting a relegation battle in the Premier League? So I would doubt that Ange would have a club such as Leicester City on his radar.
"He has rebuilt Celtic. The fans love him, and he loves the fans. It would take something special to break up that relationship. If he was linked with a top-six club down south, then that may well be a different story. That kind of thing would be a potential game-changer."