Robben said that everyone at the club is expecting to have to play at their best to get through to the semi-finals, but that it was an advantage for the German team to play away from home first.
"It's a good draw and we're away from home first," Robben told the club's official website. "United aren't in great shape but they're still a top team. We face two very tough matches.
"The best thing about Manchester is the atmosphere. All of us are in the game for the chance of playing in an atmosphere like that. Old Trafford is very special indeed and we should enjoy it.
"The fans are a 12th man for Manchester United. Obviously they're struggling in the Premier League this season but that counts for nothing in the Champions League. We have to be up for it from the start."
Robben's Bayern are currently 23 points clear at the top of the Bundesliga.