Last week's draw against West Brom means Spurs are four points behind fourth-placed City with five matches remaining. Defeat to Chelsea on Saturday and a victory for Roberto Mancini's men over West Ham the following day would severely dent the Londoners' hopes of qualifying.
"We need to go to Stamford Bridge and win. It will be a tough game but we have to try and pick up three points to stay in that race," Redknapp said. "Man City are in pole position now but it's all to play for. We have to be positive and win as many as we can. It can still be done. "
To make matters worse for Redknapp, Spurs have to travel to Eastlands and Anfield after this weekend's trip to a ground where they have not won since Gary Lineker and David Howells helped them to a 2-1 win over their west London rivals in 1990.
But having seen his side pip the Eastlands club to fourth last season, Redknapp is confident of taking three points off Chelsea in order to put Tottenham back in this year's hunt for fourth.
He added: "The idea is to be in striking distance when we go to Man City (on May 10). We have some tough games coming up but I still think it will go down to the wire."
The Spurs boss has never hidden his dislike of the Europa League and admits the possibility of competing among Europe's second tier fills him with dread.
"Our first year in the Champions League has been hard. It has taken its toll but the Europa League takes a bigger toll," Redknapp said.
"Playing on Thursday and Sunday is not ideal but if that's what we end up with that's what we end up with."
Source: PA
Source: PA