Redknapp says the club must end their policy of selling their star players each summer and build a team around Bale that is capable of challenging for honours.
He told Sky Sports: "Two years ago I remember [former Manchester City assistant boss] David Platt called my dad and asked about buying Luka Modric and Gareth Bale. It's going to be exactly the same again.
"I've played for that club and I've seen it year in and year out that they sell their best players. Michael Carrick had a great season and they decide to sell him. Dimitar Berbatov? They sell him. Luka Modric? They sell him.
"Why don't they keep hold of their best players? Why don't they change the structure and go and give Gareth Bale what he would get if he was to go somewhere bigger.
"He might want Champions League football, but he also might want to be a big fish in a small pond. I've met Gareth plenty of times and he doesn't strike me as that sort of a boy.
"I just feel that he can still develop there and get even better and Tottenham can build a team that can challenge for the Premier League."