You would think it was the natural habitat of a team known as 'The Devil'.
The bemused expression worn by Mario Balotelli on the front page of Sunday's Gazzetta dello Sport suggested otherwise. "Milan, che inferno," read the headline: Milan in hell.
In this case hell was not the terrifying, nine-circled version envisioned by Dante. It was the San Siro car park, where Balotelli and his team-mates found themselves confined late on Saturday evening after a game they had to win "at all costs", as midfielder Andrea Poli had put it.
Having painted themselves into a corner with strident pre-match comments like that, the honest mid-table toil of Genoa proved too much for Milan to overcome, earning only a point despite Kaka having given them the lead in the fourth minute, despite the visitors being reduced to 10 men in the 35th minute, and despite Milan being awarded a penalty which, for only the second time in his career, Balotelli missed.
It was all too much for a group of 300 irate fans, who blocked the stadium exits, only 'permitting' the team to leave after a small delegation led by Kaka and Christian Abbiati had emerged to promise more effort and fewer nightclub visits: a solemn sacrifice for any Italian footballer to undertake.
If claims made before Celtic's first meeting with Milan about there never having been a better time to face them now seem misguided after a 2-0 defeat, it is because now, not then, is surely the ideal time to face them. The statistics provide a stark portrayal of a crumbling empire. Milan have made their worst start to a league campaign since 1981/82 and are on their longest winless run - five games - in Serie A since 2007. They have won just two of the 13 games played in all competitions since that matchday one encounter with Neil Lennon's side, and both were unconvincing 1-0 victories, at home to mid-table opposition, and secured by Valter Birsa goals. Ironic, given that the Slovenian midfielder is often held up as a symbol of the club's declining standards.
With five points to their name and a home game against Ajax still to come, Milan's hopes of knockout qualification could survive defeat at Celtic Park tonight, but could Massimiliano Allegri? "We'll go forward with Allegri," promised the chief executive Adriano Galliani after the 0-0 draw at Chievo earlier this month, one of many pro-Allegri statements made by Milan officials of late, but this is a club renowned for its use of doublespeak in recent years.
Allegri continues to be stalked by the shadows of Pippo Inzaghi and Clarence Seedorf. Both men played under him as recently as last year and are joint favourites to replace the Tuscan as coach.
Allegri's situation is just one of the problems enveloping Milan at present. While not as severe as it was at the time of Celtic's San Siro visit, their injury crisis is far from over. In the boardroom, Barbara Berlusconi, daughter of President Silvio and 'Director in Charge of Special Projects', is increasingly influential. If reports are to be believed, her current special project is removing Galliani.
Then there's Balotelli. Injured and suspended so often this season that he has featured in just eight of the Diavolo's 13 Serie A fixtures, the former Manchester City forward tweeted the words "This is the end" at 3am on Sunday, prompting a wave of speculation about whether he was referring to his future, Allegri's future, or simply watching the Seth Rogen comedy bearing that title.
None of this entitles Celtic to complacency, of course. Milan's Champions League displays have been fairly decent, particularly in the double-header against Barcelona. And any team containing Kaka and Balotelli will always have a puncher's chance. But when simply getting in and out of the car park without any hiccups constitutes success for your opponents, you cannot help but be confident.
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