The Bhoys failed to secure a historic tenth consecutive Scottish Premiership title, with bitter rivals Rangers 20 points clear at the summit.
In response to Celtic s underwhelming campaign, manager Neil Lennon parted company with the club in February, with his assistant John Kennedy taking charge for the rest of the season.
As well as Lennon’s departure, the Hoops are facing the impending exit of club captain Scott Brown and chief executive Peter Lawwell, as well as head of football operations Nick Hammond, in what is now becoming a significant summer of change in the east end of Glasgow.
And Dalglish has been quick to point out just how much of a challenge his former club are facing in the coming months.
Speaking to talkSPORT, he said: “Whoever’s making the decision on who’s going to get the [manager’s] job, as long they’re happy with them, that’s it.
"That’s the only person’s opinion that matters.
"They’ve got a big season, a big close season.
"They’ve appointed a new chief executive. Peter Lawell, who did a fantastic job, has retired. They’ve got to get a new manager. They’ve got to get a new director of football.
"Which do they go for first, the director of football or the manager?
"It’s not easy. There might be a guy who you fancy as manager, but the manager doesn’t fancy who you think you’re going to bring in as director of football.”