The right-back came off at half-time during United's 4-1 win over Aston Villa on Saturday with a thigh strain.
Better news for United was that defenders Rio Ferdinand, Chris Smalling and Jonny Evans - who all missed Saturday's game - took part in the 15-minute open training session at Carrington.
Left-back Alex Buttner ended the Villa game with a tight hamstring but trained alongside winger Antonio Valencia, who missed Saturday's game with a knee injury.
The only other absentees from the session were injured striker Robin van Persie, the suspended Patrice Evra and midfielder Tom Cleverley.
With Evra missing out, Buttner is looking forward to a chance to play against the European champions after acquitting himself well in United's recent Premier League wins over West Ham and Villa.
"I am starting to get a good feeling because I thought I played well against West Ham and Villa," he said.
"It is a big game on Tuesday but it is a chance for me to show what I can do.
"It has been vital for me to get the two matches because it would have been difficult not to play and then to have to face a big game like Bayern.
"I feel confident about playing them. I know what Arjen Robben can do and I am ready for him. I know enough from what I have seen to know how he plays the game. It is not under discussion how good he is, we all know that.
"This kind of big game is why you play football. It is what it is all about and it would be good for my career if I could do well against Robben.
"In the last two matches I have played well, put in some good challenges and I hope I will be able to build on that, not just against Bayern but after that as well."