The Hoops went down to a 2-0 defeat at the hands of Manchester United on Saturday to leave them seven points adrift with just 11 games remaining this season.
However, with several games against struggling rivals still to play, the former Tottenham boss has not given up hope of keeping the west London club in the top-flight.
"At Portsmouth I had a crap team but we got 20 points from 10 games and stayed up. It isn’t impossible," Redknapp told reporters.
|4/1||QPR are 10/1 with BetVictor to beat the Premier League drop this season
"There’s enough games left, there’s 11 games. It is wide open. We have got to go to Villa, we have got to go to Reading, we have got Wigan here.
"I still fancy us. We’ve got nothing to lose, everyone thinks we are gone [but] you can change it so quickly."
The ex-Pompey boss celebrates his 66th birthday next weekend as his side take on another of his former clubs, Southampton, and Redknapp wryly predicted a rough afternoon for himself at St Mary's Stadium.
He joked: "I’ve been thinking to myself, 'There is no better way to spend my birthday than spend 90 minutes getting abuse at Southampton Football Club'.
"They’ll be calling me ‘scummer’ because of my time at Portsmouth. That is a great way to spend my 66th birthday."