Walcott scored twice for Arsenal against Spurs on Sunday and is out of contract in 2013.
Arsenal could be tempted to sell the England international, with Redknapp hoping to reach a deal for the 22-year-old, according to a report in The Express.
A close friend told the Daily Express “Harry loves Theo. He would love to manage him again for Spurs or England.”
Redknapp had given Walcott his debut for Southampton as a 16-year-old and sees a lot of potential in the winger.
Tottenham chairman Daniel Levy will offer Redknapp a new contract to keep him and will stump up the £10million for Walcott in the summer.