Redknapp, speaking to 230 guests at a Jewish Care business breakfast in Chigwell, said: "We're right in there and have got a great chance. Manchester City are the team to watch out for."
Redknapp was also full of praise for rivals Arsenal, who have hauled themselves right back into the title race.
"They have an excellent youth set-up, a conveyor belt of young players coming through," said Redknapp.
"The gap is closing. We're trying to turn it around but it's not easy. There's not a million miles between the teams. I don't think that there will be much of a gap at the end of the season.
"Arsenal can win the title. They are a very well run club and the manager has done a good job."
But while Redknapp remains confident that his side can smash their way into the top four this season, he is not so upbeat about the future of the English game.
"Good, young British footballers are a dying breed," warned Redknapp. "We're seeing more and more foreign players and foreign owners.
"Soon it will come to the point where every Premier League club has foreign players and owners. They come from a background where they are all winners but the problem is that there can only be one winner.
"The standard of kids is not as strong as in the past as there are so many different things for them to do. In my day we only played football.
"We need to improve recruitment. There's not a massive amount of talent around in this country but it's still out there. Nothing gives you more pleasure than seeing them come right through the youth policy. They have real feelings for the club."
Redknapp's fear over the future of England's next generation of stars was mirrored by his concern for the national team.
The Spurs boss believes England, under Fabio Capello, have a great squad capable of winning the World Cup for the first time since 1966. But he worries for England's chances for 2014.
"We've got a great chance of winning the World Cup but after this group of players I'm not so sure that the future looks good," said Redknapp.
"If we don't win the World Cup, I'm sure that Fabio Capello will get slaughtered. He's about the only manager not to have suffered abuse."
Barclays Prem To Be in Top 4 Win Outright: Tottenham 3/1