There is a hubbub of press, one teacher wears a Liverpool scarf; her colleagues gather round as he is cloaked in the sort of anorak that traditionally forms an extra layer of skin for the football coach. There is a clamour for answers, for autographs, for photographs.
King Kenny surveys it all with the relaxed air of someone who accepts this is not merely his duty but his fate. At 61, Dalglish retains that crop of light hair, that sturdy body and the suspicion that every question from his majesty's press requires the services of a bomb disposal expert.
His visit to Netherlee Primary School on the south side of Glasgow is to promote an initiative in grassroots football but Dalglish has a hinterland that means he can talk on a range of subjects. His authority is gilded by experience.
With 102 caps, he has a claim to being Scotland's greatest player, he performed with unparalleled distinction at Liverpool and with brilliance at Celtic. He later managed both clubs, winning a double with Liverpool, and also took Blackburn Rovers to a Premiership title. His views are urgently sought.
King Kenny plays this role in the no-nonsense manner most commonly referred to as keeping the ball on the deck. His answers are considered, but also revealing. Dalgish is a man from the world of old football who has to deal with the realities of new football.
He has, of course, an educated foot in both fields. As the children clatter in from their exertions on the pitch, Dalglish recalls that his upbringing in the sport was hardly a world away from the class of 2014.
"It is basically the same," he says. "You have someone giving up their time to make sure that those much younger than themselves can have a game of football. The people who are doing it nowadays are exactly the same as the people who were doing it when I was growing up. The people who do it do it because they love it."
But who had the honour of giving the young Dalgish his first coaching lesson more than half a century ago?
"It was my dad that was the first person I can remember in football, kicking the ball about with him," says Dalglish of a childhood in Milton and then Govan. "You take your lead from your parents and move in from there."
He moved on to some effect, with baubles strewn across a playing career: six titles with Liverpool, four with Celtic, three European Cups in his time at Anfield.
He is asked about the quality of the current Celtic side who could achieve an unbeaten record in the SPFL Premiership and set an extraordinary mark for clean sheets.
"It's possible to go through the season undefeated because they have not lost yet and they are past the halfway mark. But the nearer you get to the finishing line, the harder it gets," he says.
"Neil [Lennon] has done a fantastic job. I suppose whatever they achieve in Scottish football will be undermined because Rangers aren't as strong as what they were in years gone by. I think that's a fair assumption but Celtic can only beat what is in front of them."
However, he adds: "It's also a great credit to Celtic that, when Rangers haven't been there, they have qualified for the group stage of the Champions League. That is a hell of an achievement for a Scottish club."
He adds of Lennon: "He's had players go out, players come in . . . he's constantly changed teams and they're still winning, so he's not doing too badly."
He is similarly supportive of Gordon Strachan as the Scotland manager though he is cautious of predicting qualification for the Euros in 2016 despite the increase in participants. "Scotland never make it easy," he says with the knowledge of both a player and a fan.
He is more outspoken on the customs of new football and of modern life. He reflects that the landscape has changed for children who now have to be supervised to play in safety. "Your mother washed the strips, darned the socks and everybody chucked in to help," he says of the old days, adding: "but nowadays because of the way society has gone if you are a parent you do not let your kids go to school themselves. It is the same with football or whatever sport they play. It is not anyone's fault, it is just the way society is."
It is said with the philosophy of acceptance. He reserves the harshest words for the modern morons, those who subjected Lennon to abuse at Tynecastle on Saturday.
He does not believe they will force Lennon out of the game, saying: "I don't think it will come to that, because the people who organise the security at the grounds will have the video to identify the culprits, get them in, bang them up, let them suffer. It's in their hands more than anybody else's then that puts everybody else off doing it."
It is the judgment of the King. It would surely win the acclaim of the masses.
Kenny Dalglish, McDonald's head of Scottish football, was speaking at the launch of 2014 SFA grassroots awards.