The Rs are currently bottom of the Premier League table, with 20 points to their name and just 10 games left, the first of which is at home to Sunderland on Saturday.
But Redknapp's men gave their chances a boost with a 2-1 win at Southampton last weekend and the experienced boss thinks five more victories and a pair of draws could be enough to save them.
"I've been optimistic all along," he said. "I still feel we'll stay up. We just need to go on a run, we need five wins at least, I think.
"I would take 37 points here and now, I'd take my chances on that if I was offered it. We just have to keep picking up results.
"We need back-to-back wins, it's about time we did it. If we can do that, it puts us right back in the picture."
With regard to Saturday's game, Redknapp says he will make a late decision on whether goalkeeper Julio Cesar and forward Bobby Zamora are fit enough to play.
"We're waiting on them and we're not sure on either," he said. "We'll leave it until the last minute.
"Zamora is obviously a big threat and we'd love him to be fit but Jay Bothroyd and Loic Remy both scored last week, so we'll see how we go.
"Sunderland are strong up front and have two very good strikers but we're at home and need to give our fans something to shout about. We're still in there with a good chance."