Barcelona, beaten 2-1 at home by debutants Rubin Kazan last time out, visit the same team on Wednesday knowing that another defeat would put them out of the top two in Group F.
The group stage's fourth round of matches could also be crucial for the fortunes of former champions Bayern Munich and Liverpool, currently out of the top-two places in their groups.
Bayern host French champions Girondins Bordeaux in Group A and Liverpool, who have lost six of their last seven games, travel to Olympique Lyon in Group E.
Real playmaker Kaka returns to the San Siro stadium for the first time as the Spaniards visit his old club hoping to avenge their 3-2 defeat at the Bernabeu.
That result prompted a dramatic turnaround in the fortunes of the two sides.
AC Milan's rookie Brazilian coach Leonardo, who went into the game under severe pressure, is now sitting pretty after an unbeaten seven-match run while opposite number Manuel Pellegrini is feeling the heat.
"Real is a game which you especially prepare for. We hope to maintain our high level of play," Leonardo said.
Pellegrini's position was questioned after Real's embarrassing 4-0 defeat by third-tier Alcorcon in the King's Cup made it three games without a win.
A 2-0 La Liga win over Getafe on Saturday, courtesy of two goals from unsung Argentina striker Gonzalo Higuain, calmed the waters a bit.
But defeat on Tuesday could see another storm brewing for Pellegrini, who will again be without injured Cristiano Ronaldo.
"The papers have been full of names of great coaches but we are happy with Pellegrini and we are sure he will finish the season positively," club president Florentino Perez told Italian television.
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Milan and Real top Group C with six points, three ahead of Olympique Marseille and FC Zurich who meet in France.
Barcelona travel to Russia having had their league lead over Real slashed to one point following a 1-1 draw at Osasuna.
Rubin Kazan, Barcelona and Dynamo Kiev each have four points in Group F with Inter on three.
Inter, seven points clear at the top of Serie A, have not reproduced their league form in Europe where they have drawn all three games.
Other teams seeking a first win are Maccabi Haifa, Debrecen, VfB Stuttgart, Rangers, Besiktas, Apoel, AZ Alkmaar, Standard Liege and Atletico Madrid.
Crisis-hit Atletico, on just one point in Group D, are unlikely to improve their record when they host in-form Chelsea on Tuesday.
Chelsea beat the Spanish side 4-0 two weeks ago and have scored 13 goals without reply in three domestic games since.
Carlo Ancelotti's team have nine points, one of four teams with 100 per cent records
