The West London side are currently 10 points adrift of safety in 19th place with just five games remaining.
Fellow strugglers Stoke City visit Loftus Road this afternoon and Redknapp said that the encounter is one of four they must win if they have any chance of survival.
"The dream is still alive," Redknapp told reporters. "It's not dead yet and we've got to keep going. We need four wins and a draw from the final five to have a chance.
"We all know it's a tall order but if it happens it may be enough to stay up.
"We have to beat Stoke and then we must win at Reading. Then we have to beat Newcastle and Arsenal, for sure. And then we have to get something at Liverpool."
QPR lost 1-0 to the Potters at the Britannia Stadium in November.