The London side, along with Reading, are adrift in the bottom three and their fate could be sealed if they lose at home to fellow strugglers Stoke City on Saturday and Aston Villa pull off a shock victory at leaders Manchester United on Monday.
Since a mini-revival in early March when they won successive games against Southampton and Sunderland, Rangers have lost three and drawn one of their last four.
They are 19th and 10 points adrift of safety but Redknapp said they had not given up hope.
"The dream is still alive. It's not dead yet and we've got to keep going. We need four wins and a draw for the final five to have a chance," Redknapp told reporters on Friday.
"We're still not down. We've still got five games to go. We all know it's a tall order but we will keep going.
"If (relegation) happens, we've got to re-group and come back stronger, but we're not giving up yet, we've still got a chance."
Rangers striker Bobby Zamora is still suspended, winger Shaun Wright-Phillips is out for the season with an ankle injury but midfielder Stephen Mbia, left out of last weekend's 2-0 defeat at Everton by Redknapp for fear of the defender picking up a fifth booking and a ban, could return.
A miserable run of form this year has plunged Stoke into a precarious position, with one league win in 13 in 2013 threatening to end their five-season stay in the top flight.
Stoke sit 16th, three points above the drop zone and manager Tony Pulis believes another six points will guarantee his side safety.
"It doesn't matter whether they come in the next two games or the last two," he told the club's website.
Pulis said Stoke needed to sharpen up in both penalty areas to arrest their slide.
"It's been in both boxes that we've struggled. Of late, we've given poor, poor goals away and we've got to stop doing that.
"And at the other end of the pitch, there have been games where we've had great opportunities and not taken them."
The Daily Telegraph on Friday reported that Stoke were trying to offload winger Jermaine Pennant following an alleged bust-up with Pulis.
The newspaper said Pennant had trained away from the club for two weeks after a row with the manager following the defeat by Everton last month.
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