The 25-year-old Croatian is reportedly keen on moving to a Champions League side, even though Spurs chairman Daniel Levy has declared him not for sale.
Man United and Chelsea have been tapped as potential suitors, with Levy accusing the latter of making an illegal public offer for the player.
"I think we have to show him our ambition, which we will do," Redknapp told Sportsweek today. "If we can add one or two good players to our squad there's no reason we can't have another great season. So Tottenham could be a great club for him to stay with for the next few years. That's what we're hoping for."
Redknapp added that keeping Modric would be key to the club's future growth. "We have to do something to keep him at the club," he continued. "We can't afford to sell Luka Modric if we want to be a successful club."
Of Modric's ambition to compete in the Champions League, he added: "I suppose he's seen a massive contract and the chance to win the Premier League and play in the Champions League and that's what he wanted. But we want that as well. We want to get back in the Champions League and we need him to help us do that."
Spurs eventually finished in fifth place last season, missing out on a Champions League spot but securing entry into the Europa League.