The reigning champions will travel to Old Trafford on Tuesday evening, where they beat United on away goals at the same stage of the competition back in 2010.
Fletcher has said that David Moyes's side are determined to put in a good performance.
"I can't wait for it," he told United's official website. "What an occasion it's going to be. It's a Champions League quarter-final at Old Trafford against Bayern Munich – it doesn't come any bigger than that.
"We've got to get up for this game and really believe in ourselves. And we will. We're really looking forward to it. Everyone is writing us off but we've got some good players here who will be desperate to do well."
United beat Olympiacos 3-2 on aggregate in the previous round.