The 30-year-old Dutchman scored one of his best career goals at the venue almost four years ago, securing Bayern's passage to the semi-finals with a sweet volley.
"It's always fantastic to play in England," Robben told fcbayern.de. "And Old Trafford has got something particularly special about it, a fantastic atmosphere.
"As a footballer, you dream of playing Champions League quarter-finals in such atmospheres."
According to Robben, Bayern can expect their stiffest test yet against the Red Devils, even if the Bavarians are unbeaten in 53 Bundesliga matches and have only lost once in all competitions in the past 12 months.
That defeat came to United's city rivals Manchester City in what was nonetheless a dead rubber final group game for both sides, who had already qualified for the last 16.
"We've got to watch out," Robben said. "The media and public opinion is that Manchester are not in good shape and that we're going through to the semis, but I don't like that at all.
"It's going to be a tough duel. We've got to be at our best from the very first minute because you only need to get distracted for a second, and you lose against Man U.
"If you lose concentration and lose the ball, then you get punished there."
Both sides will be without key players, with United deprived of Robben's compatriot Robin van Persie and Bayern without midfielder Thiago.
"It's a shame that he's (Van Persie) going to miss out," Robben said. "Everybody wants to be involved when you get towards the end of the season and it's painful when you can't be - and I know that from experience.
"Of course Van Persie has particular quality, but Manchester still have enough options up front: Rooney, Welbeck, Nani, Valencia.
"Like I said, it's going to be a difficult duel, but we're all really looking forward to it."