Robben, who pulled a calf muscle in Bayern's 2-1 loss to VfB Stuttgart on Saturday, will play only if fully fit to avoid a longer-term injury as the team are also in the running for the Bundesliga and German Cup, coach Louis van Gaal said on Monday.
It is also unclear whether French playmaker Franck Ribery, recovered from an ankle injury, will be on the pitch from the start or will come on as a substitute.
Bayern will certainly be without suspended midfielder Bastian Schweinsteiger.
"I don't know if Robben and Ribery will play but I will have to plan against them," Manchester United coach Alex Ferguson said on Monday.
United, in a record 11th Champions League quarter-final, have no injury scares with striker Wayne Rooney and defender Rio Ferdinand rested over the weekend as they attempt to make their fourth consecutive Champions League semi-final.
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In the other quarter-final match of the day, Olympique Lyon need to come out on top in the first ever Champions League all-French tie against Girondins Bordeaux to make their first semi-final appearance.
Lyon, who won seven Ligue 1 titles in a row before seeing Bordeaux break their run last season, are almost at full strength.
Bordeaux, who lost their League Cup final to Olympique Marseille 3-1 on Saturday, will be without suspended holding midfielder Alou Diarra and defender Marc Planus, who is nursing a knee injury.
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