And it is certainly not a patch on any of the great Milan sides to have lifted the continent's premier club competition, be it the European Cup or the Champions League.
Coach Massimiliano Allegri has, too, got serious injury problems and is missing several key players.
He will not be fielding his strongest team this evening.
But having said all that, AC Milan remain a top Italian side. And the standard of their reserve players is pretty high.
Kaka is out. But to be honest, I do not know if that is a huge blow to Milan. Allegri is not expecting the Brazillian to be the same sort of player, an on-pitch leader, as he was in his first spell at Milan.
A far greater loss to my mind is Stephan El Shaarawy.
The young striker carried his club almost single-handedly in the first half of last season when they were experiencing all sorts of problems.
The Italian internationalist was nothing short of sensational at that time. He is interesting many of the biggest clubs in Europe. It is very much to Celtic's benefit that he is absent.
Yet, the player who will probably come in to replace him is fairly useful too. Alessandro Matri gave the Scottish champions a torrid time when he played for Juventus in their Champions League last 16 tie last season.
He scored both home and away. Elsewhere, Mario Balotelli, the former Manchester City man, can also start.
He is certainly unpredictable. But, on his day, he can perform at a very high level.
Robinho, another former City star, can also turn it on when he is in the mood. So, as you can see, the Celtic defence is in for a difficult night.
Allegri likes to play a variation on a 4-3-3 formation. It can often be a 4-3-1-2. I would not be surprised to see Robinho playing just off a front two of Balotelli and Matri.
Nigel de Jong, the ball-winning, tough-tackling Dutchman plays in central midfield and creates a platform for those ahead of him.
If Milan have got a weakness at all then it is at the back. It is a far cry from the days when they could field Allesandro Nesta and Paolo Maldini.
I think Neil Lennon will have seen in the game against Torino he attended at the weekend - when they were lucky to come from 2-0 behind to draw 2-2 - that this team has a soft centre.
Lennon has players who can score at this level and I expect to see goals from both teams. I am sure that the Celtic manager, players and supporters will all enjoy the experience enormously.