With Ajax facing the tricky task of stopping Barcelona, Neil Lennon could see his side jump from fourth to the qualification spots if they defeat Massimiliano Allegri's outfit
Celtic – who have won 16 of their 23 home fixtures in the group stage of Europe's premier club competition – sit 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 their unbeaten Scottish Premiership record to 16 matches on Saturday, as Derk Boerrigter and Kris Commons scored in injury time to give them a 3-1 home win over Aberdeen, putting them five points clear at the top of the table.
Celtic - who lost 1-0 at Ajax in their last Champions League fixture – have won four of their 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 they 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 have made a sluggish start to their 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 their away form - they have not won in nine matches on the road in all competitions, losing four and drawing five.
A lengthy injury list has also hampered them, 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 have not won on their last four trips to Scotland and could finish the match at the bottom of the group if results go against them.