Rangers go into their Loftus Road clash with the Premier League leaders still anchored to the bottom of the table and seven points from safety.
But Redknapp has pointed to the shock 1-0 victory over West London rivals Chelsea and the draw with his previous employers Tottenham as proof they can avoid defeat against the Red Devils.
"You can't predict results," Redknapp told the Fulham Chronicle.
"We're playing Chelsea away on the back of being smashed to pieces by Liverpool. What's the score going to be you might ask? 3-0, and 4-0 to them? I was surprised as you were.
"We then play Tottenham at home who've beaten everybody away and have scored in all away games - and they don't score against us."
With other decent results picked up in the hunt for Premier League survival, Redknapp insists QPR will not be overawed when they tackle Sir Alex Ferguson's side.
"Against Man City who are champions, we get another great point and then another at West Ham, which is a hard place to go," he said.
"So we're just as capable of getting something against Man United as anyone else."