The west London strugglers are 10 points adrift of Premier League safety and need to win four of their five remaining fixtures to have any hope of retaining top-flight status.
Relegation could be sealed as early as this weekend if QPR fail to beat Stoke at Loftus Road and Aston Villa surprise Manchester United, but Redknapp is not giving up hope of pulling off a miraculous escape.
"The dream is still alive. 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," Redknapp said.
"While it's still possible we've got to keep believing and keep going. If we could win four and draw one - we all know it's a tall order but if it happens it may be enough to stay up.
"This season 37 points may be enough to keep you up, so we have to keep trying.
"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. It's tough, but that's the dream and while it's still there we have to keep going.
"Achievement-wise doing that would be the best. You would love to be able to do that for the people who own the club. I find it so sad because they're lovely people."