With Ajax facing the tricky task of stopping Barcelona, Neil Lennon could see his side jump from fourth to the qualification spots if it defeats Massimiliano Allegri's outfit.
Celtic – which has won 16 of its 23 home fixtures in the group stage of Europe's premier club competition – sits bottom of Group H but could move up to second and into the qualification spots with a victory and if Barcelona beat Ajax.
Neil Lennon's side extended its unbeaten Scottish Premiership record to 16 matches Saturday, as Derk Boerrigter and Kris Commons scored in injury time to give ut a 3-1 home win over Aberdeen, putting the team five points clear at the top of the table.
Celtic - which lost 1-0 at Ajax in their last Champions League fixture – has won four of its five home matches in this season's competition.
Wins over Cliftonville, Elfsborg and Shakhter Karagandy in qualifying were followed by a 1-0 defeat against Barcelona, but the Bhoys rebounded with a 2-1 triumph over the Eredivisie champions last month.
Georgios Samaras and James Forrest have scored three goals each in the Champions League this season, while Scotland midfielder Kris Commons has weighed in with two, in addition to his six league strikes.
Milan beat Celtic in the reverse fixture at San Siro earlier in the season, as Emilio Izaguirre's own goal was followed by Sulley Muntari's late strike, giving the hosts a 2-0 success in September.
Adam Matthews (broken collarbone) and Steven Mouyokolo (Achilles) are sidelined for Tuesday's match.
Similar to last season, Milan has made a sluggish start to its campaign, with Massimiliano Allegri's men having claimed just 14 points from 13 Serie A matches.
That leaves them in the bottom half of the table, with their latest disappointing result seeing them held to a 1-1 home draw against a 10-man Genoa on Saturday, in which Mario Balotelli missed a penalty.
Key to Milan's struggles has been its away form - it has not won in nine matches on the road in all competitions, losing four and drawing five.
A lengthy injury list has also hampered it, with the absence of Stephan El Shaarawy (thigh) in particular a big blow, with the forward having not played for his club since September 1.
Fellow forward Giampaolo Pazzini (knee) has been missing since May and defender Mattia De Sciglio has played just once since August due to a persistent knee injury.
Goalkeeper Marco Amelia (knee) and Cristian Zaccardo (ankle) also remain on the sidelines.
Milan has not won on its last four trips to Scotland and could finish the match at the bottom of the group if results go against it.