David Moyes's men beat Olympiakos 3-0 last week to seal a 3-2 aggregate victory and were subsequently drawn against the current holders of the competition on Friday.
Bayern sit 23 points clear at the top of the Bundesliga, while United are seventh in the Premier League, but Scholes has told his former team-mates to "believe" as they look to upset the odds against the German giants – and also claimed 40-year-old Ryan Giggs will be key to their hopes.
"There's so many good players in either side, obviously United haven't had the season they would have liked and the players haven't been in the best of form," he told Goal. "Wayne Rooney will be a big player for United with Robin van Persie gone.
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"For the Bayern Munich side, I don't know where to start. There's so many top players. There's [Arjen] Robben, [Franck] Ribery, [Mario] Gotze, [Mario] Mandzukic, there's so many quality players.
"I haven’t even mentioned Toni Kroos as well. I saw the performance against Arsenal in the round of 16 and it was the best midfield performance I've ever seen.
"We'll be up against a top quality team, but we also have to believe. It will be very difficult, it's one of the teams you wouldn’t want to get but if we can beat them, who knows, we can go all the way to the final."
Scholes also conceded that United will have to win Europe's elite club competition if they are to play in it next season, as they currently lie 11 points behind fourth-placed Arsenal in the league.
However, he does not believe an enforced absence from the tournament would put off potential summer signings, as United remain one of the biggest clubs in the world.
"If we don’t qualify for the Champions League, it's looking like the only way we can do that is if we win the tournament," he added. "It will be difficult, but we have to remember Manchester United is one of, if not the biggest club in the world.
"And to sell that to new players, you just have to say that it's only a year that we are out of the Champions League, and we can bring in the quality players we want to to help us get back to where we should be.
"But I do agree it will be difficult to sign players when you are not in the Champions League. Every top player around Europe, that's what they want, they want Champions League football. But you have to hope that the pull of Manchester United is big enough to bring players in."