The Swedish defender was a member of the last Celtic side to win the domestic treble in 2001 and played for them in a European final in Seville two years later.
Throughout the dominant seasons he enjoyed under Martin O’Neill’s management, however, Mjallby could never claim the historic tag of domestic invincibility which Brendan Rodgers’ current Celtic squad are now so close to achieving.
Mjallby will be among the first to applaud a feat towards which Celtic hope to take another significant step by beating Rangers in Sunday’s Scottish Cup semi-final at Hampden. But even then, he will not yet be ready to concede that Rodgers’ side have eclipsed O’Neill’s vintage of 16 years ago.
Mjallby believes it will take another full season before the present Celtic team can be properly assessed, although he does feel they have the potential to ultimately be regarded as second only in the club’s history to the peerless 1967 European Cup winners.
For the moment, however, Mjallby insists that the domestic challenge posed to Celtic’s 2001 treble winners was far tougher than that which Rodgers and his players have faced this season.
“I would say Martin’s team of 2001 would probably beat today’s Celtic team,” said Mjallby. “I say that because of the experience we had. We were a team of grown-up boys; in fact, we were men.
“This team now is fantastic but I still think you need to give it another year before you can compare it with Martin’s team. But if they keep doing what they’re doing now, they’re going to be number two after the Lisbon Lions.
“It’s a great achievement if they go through the season unbeaten domestically. What a turnaround it has been. Months ago, we were moaning like hell when Celtic played in Gibraltar and had a tough evening in a Champions League qualifier. Now we are sitting here speaking about them being invincible, going through the season without losing a domestic game. What a fantastic achievement that would be.
“It just shows how well Brendan Rodgers has done. What a great appointment it has been. The players he has brought on the scene, with Moussa Dembele and Scott Sinclair, it’s the Celtic way as well. They have been a great, great force going forward. I know they haven’t conceded many either but this team plays the game the Celtic way.
“I can’t really compare the two teams, ours in 2001 and this one. We have to maybe give them another season before you can say that they are a better group of players than we were.
“This is no disrespect to today’s team. I would just say that the opposition was probably harder for us in 2001. You had a very, very strong Rangers at the time and you had Hearts, Dundee and Dundee United who were probably stronger than the rest of the teams are right now. But nevertheless, it would be an amazing feat.
“Looking at the season, you have to say Celtic are favourites – not only for Sunday’s game, but to win the Scottish Cup which will mean they win the treble.
“They have had a wonderful season. Their confidence is sky-high. They have the right tempo, a lot of players are positive and have improved since Brendan Rodgers came in the door.
“But the last Old Firm game was a draw and we all know what can happen in these fixtures. Rangers will be confident they can raise their game and give Celtic a very hard afternoon.
“The new Rangers manager hasn’t changed too much yet, he’s just in the door, but they look to be quite solid in the few games they have played under him so far. They will need to be very solid defensively to have any chance of winning the game on Sunday.”
Mjallby, now manager of third-tier Vasteras in his homeland, also spent four years as assistant boss to Neil Lennon at Celtic. During that spell, he developed a greater appreciation of captain Scott Brown, who will be freed to play on Sunday by Celtic’s appeal against his red card against Ross County last weekend.
“He is always important to Celtic,” added Mjallby. “Having had the chance to work with him, he is a great player to have in your team. He is an excellent skipper. He has that energy, passion and drive you need from your captain.
“As a footballer, he is also better technically than many give him credit for. In the four years I worked with him, I was quite impressed with him whenever we did technical skills.
“He has that reputation as a running, aggressive midfielder but there is so much more to him. He is going to be great for Celtic in the coming years as well.
“I don’t think he gets the credit he deserves for the technical side of his game. I played against him when he was a young kid at Hibs, only 17 or 18, and even then you could see he would become a really good player. But maybe not this great.
“He has had a fantastic career for Celtic. Over the years, he has got more and more positive reviews and more credit.
“When I was assistant manager at Celtic, he was always being recognised for his great energy, desire and running. He was known as hot-headed, someone who will always give you everything. But after working with him, I found out there is much more to him.
“It’s great to have him in your team, not only for his leadership skills but because he is a very good footballer.”
l Johan Mjallby was speaking at a William Hill media event. William Hill is the proud sponsor of the Scottish Cup.