The seven-time European champions are yet to pick up a point in this year's league phase, while their visitors got off the mark with a close-fought victory over Sturm Graz earlier this month.
Match preview
Having succumbed to a 3-1 defeat in their first continental contest under Paulo Fonseca, losing to Premier League high-fliers Liverpool at San Siro, Milan went on to suffer another setback last time out.
The Rossoneri were beaten 1-0 by Bayer Leverkusen, as a second-half strike from Victor Boniface ensured all three points would go the German champions' way, leaving Fonseca's side empty-handed again.
Stretching back over several years, Milan have won only nine of their last 33 games at Europe's elite level, and another defeat this week would see the once-mighty side lose their first three matches of a Champions League campaign for just the second time to date.
At several different clubs, Fonseca has now won only one of his last nine in UEFA's top club competition, and he is sorely in need of another win on Tuesday evening, given a mixed start to his stay at San Siro.
On their return from the international break, Milan beat Udinese 1-0 at the weekend - recording just their fifth win in 19 games via Samu Chukwueze's early goal - despite playing over an hour with 10 men after the dismissal of midfield dynamo Tijjani Reijnders.
As a result of that determined display, the Rossoneri remain undefeated through four home fixtures in Serie A this season, winning each of their last three without conceding a goal.
Following their 1-0 victory over Sturm Graz at the start of October, Club Brugge can travel to Italy's second city boasting a similarly impressive away record during the past year - certainly in the Champions League.
The Belgian side have not lost any of their last four group or league games on the road - all without shipping a single goal - while two previous visits to Milan also brought clean sheets.
After a goalless draw in the 1990 European Cup, the Blauw-Zwart enjoyed a memorable 1-0 Champions League win at San Siro 21 years ago, which they will hope to replicate in midweek.
Having lost their opening game of this campaign to last season's beaten finalists Borussia Dortmund, Nicky Hayen's side bounced back by winning in Austria thanks to a fine first-half strike from Christos Tzolis, boosting belief that a playoff place is not beyond them.
Most recently, Saturday's 2-1 league win over Westerlo moved Club Brugge up to fourth place in the Pro League standings, four points behind early leaders Genk.
Now, a big week awaits the Belgian champions, as after facing down Milan they must return home for a high-profile clash with old foes Anderlecht at Jan Breydel Stadium.
AC Milan Champions League form:
L
L
AC Milan form (all competitions):
L
W
W
L
L
W
Club Brugge Champions League form:
L
W
Club Brugge form (all competitions):
L
L
D
W
D
W
Team News
Paulo Fonseca shuffled his pack for Saturday's gritty win over Udinese, so further changes should be expected against Brugge; most notably, French full-back Theo Hernandez will be available after serving a Serie A suspension.
Only Ismael Bennacer (ankle), Alessandro Florenzi (ACL) and Davide Calabria (calf) are certainly sidelined by injury, with recent Italy call-up Matteo Gabbia hopeful of overcoming a muscular problem.
Alvaro Morata will vie with Tammy Abraham for selection up front - though they have occasionally been paired together - while Rafael Leao could be recalled. Samu Chukwueze, Noah Okafor and this term's star man Christian Pulisic are also contending for places in the final third.
Meanwhile, Club Brugge may be missing Denmark forward Andreas Skov Olsen, who is struggling with a calf injury, while Gustaf Nilsson (Achilles tendon) and Casper Nielsen (fitness) are doubts for Tuesday's game.
Dutch full-back Bjorn Meijer recently returned to full training following several months on the sidelines after knee surgery, but he is not expected to feature yet.
Belgium international Maxim De Cuyper - scorer of a superb goal against Italy in the UEFA Nations League last week - is therefore set to start on the left side of a back four, ahead of veteran goalkeeper Simon Mignolet.
AC Milan possible starting lineup:
Maignan; Emerson, Tomori, Pavlovic, Hernandez; Fofana, Reijnders; Chukwueze, Pulisic, Leao; Morata
Club Brugge possible starting lineup:
Mignolet; Seys, Spileers, Mechele, De Cuyper; Vetlesen, Onyedika; Skoras, Vanaken, Tzolis; Jutgla
We say: AC Milan 2-1 Club Brugge
On home soil, hit-and-miss Milan are generally much tougher to beat, despite their obvious frailties.