Spurs moved in to third, nine points behind leaders Manchester City, on Monday night with a comfortable 2-0 win over Aston Villa at White Hart Lane.
Tottenham finished fifth last year after running out of steam half way through the season, but Redknapp insists his team will challenge for the title if they keep playing the way they are at the moment.
Harry Redknapp: "The title is a possibility. It's not impossible.
"When I came here I said I wanted to get in the Champions League.
"It's not impossible for anyone. If you keep winning matches and believe in yourself you'll do it.
"Last season Man Utd won it because everyone fell over. If we keep up the form we're in at the moment we'll win the league, but that will be very hard."