Madrid's desire to win a record 10th European Cup title has turned into an obsession in recent years but their bid to lift the trophy this year suffered a blow when they were drawn against runaway Premier League leaders United in the last 16.
Higuain knows Sir Alex Ferguson's side pose a serious threat to their hopes of making the quarter-finals but also believes the Spanish giants have the class and ability in their squad to really hurt their English counterparts.
He told the Bwin website: "They (United) are quite a compact team. They always make it to the knockout rounds in European competition and we're going to have to be on our toes.
"But we can do a lot of damage with individual quality and with counter-attacks, although we can't forget we need to have a solid defence, a winning mentality and team-spirit."
The 25-year-old Argentina international, who joined Madrid from River Plate six years ago, also stressed the importance of trying to keep a clean sheet in this week's first leg.
He also urged the Bernabeu faithful to get behind Jose Mourinho's men, who are looking at the Champions League and Copa del Rey for glory this season after seeing their Primera Division title defence all but ended following a disappointing first half to the season.
"Our goal must be to win and if we don't concede then so much the better. We know that an away goal can really influence things," he said.
"We also want our fans to get behind us. The team always tries to do its best, sometimes it goes well and sometimes it doesn't.
"There's no doubt we are going to go out and give it everything."