The two sides will meet at Loftus Road on Saturday afternoon, with QPR bottom of the Premier League table and visiting United at the top.
However, despite the gap that exists between the two teams, Townsend believes that his side are more than capable of causing an upset.
"In the dressing room after we'd lost 4-1 at Swansea two weeks ago, we were still saying - 'We can beat United,'" he told the London Evening Standard.
"There is no fear there. Before I arrived, QPR beat Chelsea and drew with Manchester City, so why not? We have to think we can go in there and win the match."
The R's are currently seven points from safety with 12 matches left to play.