Bayern were huge favourites to see off Chelsea in the final at the Allianz Arena in 2012 but the Blues lifted the trophy following a thrilling penalty shootout.
United have even longer odds to overcome Bayern than Chelsea were on that night, but Neuer says his team-mates must not be complacent ahead of the quarter-final clash with David Moyes' men.
"We just have to think back to two years ago," the Bayern goalkeeper said.
"Chelsea who finished sixth and won the Champions League, unfortunately for us.
"In the Premier League there have been a number of less than convincing performances (from United) but if you look in the Champions League they fought back at Olympiacos to win 3-0 at home and that shows there's a difference (between their domestic and European form).
"If you look at the history of Manchester United, they are always a big side so there is no time of underestimating them."
Neuer knows what it is like to lose to United. The year before he joined Bayern, he came up against Sir Alex Ferguson's side for Schalke in the Champions League semi-finals.
United beat the Germans 6-1 on aggregate, but it could have been a far worse scoreline for the Germans had Neuer not put in a first-leg performance that Ferguson described as the "finest" he had seen against his team.
Speculation was rife that Ferguson wanted to sign the 28-year-old following that display, but Neuer insists he was never going to move to Old Trafford.
"It was an honour for Sir Alex to say that about me even though we lost both games," Neuer said.
"It wasn't an option coming here (to Manchester) though because I wanted to join Bayern."