Spurs and Chelsea have been vying for the final Champions League spot in recent weeks, with the champions leapfrogging their north London rivals into fourth place on Tuesday thanks to their 2-1 win over Manchester United.
City once looked destined to fight for the title but their recent poor form has left them two points ahead of Chelsea and three ahead of Redknapp's team having played one more match than both.
Banana skin: Spurs suffered a slip in their last game with a shock defeat at Blackpool
Redknapp is convinced Carlo Ancelotti's side are certain of Champions League qualification and thinks Tottenham and City are set to fight it out for fourth in a repeat of last year's contest between the two, which Spurs won.
'I don't see Chelsea not being in the top four. I felt before the Liverpool game, which they lost, that they could still win the league,' Redknapp said. 'If they had beaten Liverpool that day they would have been in a very strong position.
'They are a very strong outfit. I still think Tottenham can be in the top four, and I think it's between ourselves and Man City now.'
Spurs were level on points with City at this time last year before they won eight of their remaining 11 matches - one of which came at Eastlands - to pip the north west club to fourth position.
Grinding it out: Redknapp says City and Spurs, seen here in their 0-0 draw this season, are in a race for fourth
City have since spent around ?150million on acquiring players to beef up their squad for their domestic and Europa League campaigns. Spurs have parted with a fraction of City's expenditure to bring in the likes of Steven Pienaar, William Gallas and Rafael van der Vaart, but have still managed to make it into the last 16 of the Champions League and fight for a top four place.
That, Redknapp believes, is proof that his squad is good enough to cope with what could be a hectic run-in if they beat Milan next week.
Redknapp said: 'For us to be where we are in the league and to have had such a great season in the Champions League is a fantastic achievement so it hasn't affected us at all - we have managed to fight on both fronts and have done great.'
Spurs returned from a five-day training camp in Dubai on Wednesday ahead of Sunday's Barclays Premier League match at Wolves and the second leg of the club's Champions League last-16 tie with Milan three days later.
Battle of the bosses: Spurs manager Harry Redknapp (left) and City counterpart Roberto Mancini (right)
Redknapp's team lead 1-0 after the first leg thanks to Peter Crouch's vital strike at the San Siro, but the club's chances of progressing into the quarter-finals may hinge on the fitness of a number of key players.
Gareth Bale and Van der Vaart are likely to miss Sunday's game at Molineux with their respective back and calf injuries, but Redknapp is hopeful that they could return for Wednesday's showdown at White Hart Lane.
'I'm hoping Gareth will be fit,' Redknapp said. 'He feels ok. He has just got to push himself through it now. We'd love him back. We'll wait and see. Rafa is the same. He will not be fit for Sunday, but there is a chance he will be fit for Milan.'
Redknapp's squad has recently been hit by injuries to other key players such as Ledley King, Tom Huddlestone, Vedran Corluka and Jonathan Woodgate.
He is confident about their chances of recovery though and hopes to have a full squad available in around two to three weeks to help his side in their push for a top-four finish.
'We trained hard and the injured players worked hard with the fitness coaches and physios in Dubai,' Redknapp added. 'We are close to having an awful lot of players back fit. Within another two weeks we'll have five or six coming back which will make a big difference.'
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Explore more:People: Jonathan Woodgate, William Gallas, Peter Crouch, Harry Redknapp, Roberto Mancini, Gareth Bale, Ledley King, Carlo Ancelotti, Tom Huddlestone Places: Dubai, Milan, Liverpool, London