Woodward, who guided England to the Rugby World Cup title in 2003, was employed by the Saints as their technical support director in 2005 when Redknapp was manager.
And Woodward told The Independent on Sunday: "He's an Englishman who's proved himself and from what I saw of him, he's ideally suited.
"I learned so much. The players respect him hugely. He has this incredible talent for spotting and grooming talent.
"I hope England do well in Euro 2012 with (Fabio) Capello but after that I'd like to see Harry in charge because he is a world-class coach."
Redknapp's Tottenham are flying high this season, sitting third in the Premier League, three points behind second-placed Manchester United with a game in hand.
Source: AFP
Source: AFP