Dalglish won six league championships as a Liverpool player and half as many again as their manager. The last time the Anfield side could call themselves the best team in the country, in 1989/90, it was on his watch.
A handful of managers have come and gone since then: Graeme Souness, Roy Evans, Gerard Houllier, Rafa Benitez and Dalglish himself in a second stint. A sixth is now causing real ripples of excitement around Anfield and far beyond. Liverpool finished seventh in 2012/13, Brendan Rodgers's first season, and were a typically remote 28 points off the pace. Now? They are only six points from the top and firmly in the chase.
Chelsea are on 56 points, Arsenal 55, Manchester City 54 and then Liverpool on 50. Can they be champions? Routing Arsenal 5-1 at the weekend added to the number of converts who believe they have what it takes.
What about the man who knows better than most? Did they convince Dalglish? "The number of points tells you how well you're doing and the table doesn't lie. They are in fourth, but they are playing really well. Everyone around Anfield on match day has a smile on their face in anticipation and supporters are happy going to matches.
"What they are seeing on the pitch is heartwarming, like the Arsenal game when they demolished them 5-1. It was enjoyable for everyone who was there, apart from the Arsenal fans.
"They will just take the next game as it comes. Now that the Fulham match is on that's their next target [tonight's match at Craven Cottage was at risk before the London transport strike was called off] and they will take it from there. It's not stood them in bad stead so far. That's been the way it's always been and they are not going to change the habits of a lifetime.
"Last summer there was talk that Luis Suarez might leave. The fact is, he never left. The other fact is, he's a fantastic player. He's been brilliant this season. It's nothing to do with whether or not I've worked with him or who he compares to. He's a fantastic player this year, last year and next year. Even when he didn't score at the weekend [against Arsenal] he was terrific. He'd a brilliant shot and a free-kick that almost went in. Every game he plays there is something really positive that comes from him."
If Liverpool remain in the mix going into the final weeks of the season will it come down to whether they can hold their nerve? "It comes down to a lot of things, but the most important thing is to get into the position. Once you get there I don't see how you can be apprehensive about carrying it on. They are where they are because they deserve it.
"Would it be a good thing for the league for Liverpool to win it? If you support Liverpool, then yes. But the league doesn't need a lot of help, does it? Any team that wins the Premier League is going to be worthy champions, as Manchester United were last year.
"Anyone who wins a league of that quality is going to be worthy and deserving champions. The English Premier League is always a good race, it's just a wee bit closer this year. United won it by 12 or 13 points so it's closer, tighter and really entertaining. The more teams you have in with a shout the better it is and the more exciting it becomes."
The rise of Liverpool this season is causing the locals to break out in a cold sweat around Old Trafford. Manchester United surrendered their own hope of defending the title long ago. Their only interest in that, now, is which of the four contenders would be the lesser evil. Arsenal? Chelsea? Manchester City? Liverpool? As if United's own struggles under David Moyes were not bad enough this season, the thought of Liverpool returning as English champions is unthinkable for them.
Dalglish is far too long in the tooth to take satisfaction from even a great rivals' problems. When he was asked about Moyes' struggles this season he was measured about his fellow Scot. "He's just got to get on with the job. I don't think sympathy is what any manager wants. Sometimes when you are working it doesn't go well for you and sometimes it goes better. Nobody is wallowing in anyone's misfortune. I'm sure 'Moyesie' doesn't want sympathy. I think he'd rather have a couple of goals . . ."
Dalglish was speaking at Greaves Sports in Gordon Street, Glasgow, as he formally opened the shop's Under Armour department.