When asked about the one thing he wants to achieve for Spurs, Redknapp told Hotspur magazine: "I'd love to win trophies and try to compete for a Champions League position.
"Basically, the dream is to make Tottenham a terrific team once again."
However, Redknapp acknowledged the difficulty in qualifying for the UEFA Champions League, with Spurs having twice come close in recent years.
He added: "It's very, very difficult because the 'big four' are so powerful.
"I think you'll now see Manchester City pushing on and challenging because of all the money they've got.