Rangers head into the final 10 games of the season four points from safety and last in a Barclays Premier League table they have been looking up at for almost the entire campaign.
Victory at Southampton last weekend revived hopes of a great escape but it was just their third success in 28 league games.
Redknapp believes his side will have to win at least another five, and pick up a couple of draws along the way, if they are to have any chance of beating the drop.
That would appear a tall task for a side that have so far accumulated just 20 points and Redknapp admitted even his target of 37 points might not be enough.
"We need a run of wins. We need another five wins at least I think," Redknapp said ahead of Sunderland's visit to Loftus Road.
"We need to win half our games and get a draw or two and get to 37 points.
"I would take 37 points now and walk away. I'd take my chances.
"Whether it is going to be enough I'm not sure but if someone said you can have 37 points I think you'd have to be a fool not to take it.
"That's where we are at the moment. You just have to keep going and keep trying to pick up results."