The defending European champions were handed a last-eight showdown with David Moyes' side, who go into the clash as 28/1 outsiders for the crown.
United beat Olympiakos 3-0 on Wednesday night to overturn a two-goal first-leg deficit and secure a place in Friday's quarter-final draw but continue to struggle in their Premier League campaign.
In Sir Alex Ferguson's last season in charge United lifted a 20th top-flight crown but find themselves languishing in seventh under the tutelage of Moyes and Robben is eager to take advantage of the off-colour Red Devils.
"This is a good draw because we play the first leg away and then at home," he said.
"Manchester United are not in the best condition and I'm looking forward to the games."
However, Bayern captain Philipp Lahm remains cautious and insists the German champions cannot afford any room for complacency.
"We are the defending champions so we are one of the big favourites for the title," he said. "But United is still a big club with outstanding players.
"We must not be blinded by their position in the Premier League. The fact we play away first does not matter.
"We will go to Manchester to attack and score goals."
Former Germany international and Bayern sporting director Matthias Sammer believes United must be shown due respect and warned of the threat of Old Trafford.
"It's a highly attractive draw against an opponent who is struggling to get some stability," he claimed.
"Manchester United at home has proved, with the crowd in the stadium, that they are able to do great things.
"We would do well to speak with humility and great respect about an opponent who is highly dangerous on a good day."
Despite their present Premier League woes, striker Thomas Muller still rates United as one of England's top clubs and admits there was never going to be an easy draw at this stage of Europe's premier competition.
"Before the draw there were no opponents I would have taken gladly," Muller insisted.
"Manchester still turned up in the second round against Olympiakos with a very impressive display in the second leg - evidence of their quality.
"On paper you cannot think that they are not among England's top three."