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.
Falling short: Roman Pavlyuchenko (right) and Jermaine Defoe scored for Tottenham against West Brom
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.
'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. '
'The idea is to be in striking distance when we go to Man City (on May 10).
Losing battle: Tottenham have it all to do if they are to finish fourth
'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 abigger 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.'
Questions will be asked about whether the club will be able to hold on to their stars if they fail to make the top four.
GarethBale, Luka Modric and Rafael van der Vaart have all been linked with moves, but Redknapp insists they will not be sold if Spurs finish fifth.
'They are not for sale. If you do you sell them, you may as well accept you're a mid-table team,' Redknapp said.
'We are trying to be a Champions League team and we will not do that by selling our best players.'
Redknappalso reiterated his belief that Spurs need to sign one or two world-class players regardless of where they finish in the league.
Healso said that the club will look to offload players like Robbie Keane,Jamie O'Hara, Giovani dos Santos and David Bentley in order to trim thesquad next year.
'If you want to be in the Champions League you have to keep improving. I know that and the chairman does,' Redknapp said.
'We have lots of players out on loan, so we need to trim the squad a bit, with one or two of those moving on, and bring in one or two top players in.'
Spurs face a Chelsea team looking to extend their unbeaten run to seven league matches and cut Manchester United's lead to three points.
Denied: Heurelho Gomes saved Didier Drogba's penalty when Tottenham drew 1-1 with Chelsea in December
Redknapp is fearful that Fernando Torres is getting back to his best after finally opening his Chelsea account last week, but has been boosted by the return to form of his own talisman, Rafael van der Vaart.
The Dutchman scored twice in the draw with Arsenal and his manager admits his form will be key to his team's chances of making it into fourth.
'Rafa is in great form,' said Redknapp, who is likely to be without Tom Huddlestone tomorrow after his ankle injury flared up.
'He was outstanding against Arsenal. He is a goalscoring threat as well as a top footballer.
'We need him tomorrow and he is a big-game player. We are looking for him to turn in a big performance.'
?We'll fight for Champions League return, insists Spurs star HuddlestoneFed-up Spurs misfit Kranjcar keen on Italian switch to end misery at the LaneSpurs can derail Chelsea's title bid and keep pressure on City, says DefoeAll the latest Tottenham news, features and opinion
?Explore more:People: David Bentley, Robbie Keane, Harry Redknapp, Luka Modric, Giovani Dos Santos, Roberto Mancini, Gary Lineker, Fernando Torres, Gareth Bale, Jamie O'Hara, Tom Huddlestone Places: London, Europe
Source: Daily Mail
Source: Daily Mail