Spurs' 0-0 draw against West Ham on Saturday saw his team drop 14 points behind Barclays Premier League leaders Manchester United.
The north Londoners had an outside chance of making a late tilt at the championship until a recent run of poor form saw them drop to fifth.
"I've said I aim to win the league. Whether people believe it I don't know. They might think I'm mad but I think it is possible," Redknapp said.
"I said last year that I thought we'd get in the top four and we did it. I did not say I wanted to be in the Europa League, I said I wanted to be in the Champions League and we did it.
"There is nothing between us at the top now. There is nothing between us and Arsenal, Chelsea and Manchester United. I think the players believe it too. We have some real good players and if we can get one or two in to improve the squad, then the sky is the limit."
Source: PA
Source: PA