The 25-year-old Croatia international stunned Spurs supporters by declaring he wants to leave White Hart Lane, and will have enraged some by announcing Chelsea as his preferred destination.
Spurs chairman Daniel Levy responded by ordering the Blues to drop their pursuit of the player, insisting he was not for sale “at any price” to any club.
Redknapp now wants Tottenham to bolster their own squad and prove to Modric he does not need to join “a bigger club” to win silverware.
“I think we have to show him our ambition, which we will do,” Redknapp said. “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.”
Modric’s comments came days after Tottenham rejected a £22 million offer from Chelsea — a bid ridiculed by Redknapp — and the Spurs boss confirmed that other clubs had also expressed interest.
“Chelsea are not the only club that have been in for him,” he said. “There have been other clubs — top, top clubs. But if Tottenham are looking to go anywhere we can’t be selling Luka.
“We have to do something to keep him at the club. We can’t afford to sell Luka Modric if we want to be a successful club.”
He added: “He’s a fantastic lad. You’ll never meet a better lad than Luka. 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.
“If Daniel’s saying no he really can’t be seen to be going back on that now. He’s made a very strong statement. I wouldn’t see Daniel backtracking on that at any price.”
Modric has reportedly also attracted the attention of Manchester City and Manchester United, but Chelsea would appear to be the player’s preferred destination as he would like to remain in the capital.
Redknapp admitted the bid from Chelsea had been difficult to comprehend given they are still without a manager following the sacking of Carlo Ancelotti last month.
“It is very, very strange and difficult to understand,” he said. “But this has been going on for quite a while, not just this week. It’s been going on for the last three or four weeks. Somebody else at Chelsea is choosing the players — not the new manager.”
Jermain Defoe has also been linked with a move away from White Hart Lane — with some suggestions of a shock switch to rivals Arsenal.
“I didn’t see that,” Redknapp said of such speculation. “I couldn’t see that one happening.”