Redknapp was linked with the job when Steve McClaren was sacked, but the Football Association decided to go for a foreign coach and appoint Capello.
Related ArticlesBruce: Darren Bent will prove England credentialsTottenham v Sunderland: match previewPremier League tablePremier League fixturesSport on televisionBut Redknapp, 61, believes Bruce is a realistic candidate to lead his country.
'I think Steve can do the job, why not?' said Redknapp. 'I think he's a great guy and a good manager.
'He's done a terrific job were ever he has been, at Birmingham and Wigan. He did a tremendous job there and he's doing a terrific job at Sunderland and I would think that when the job comes around again he's the type of lad who should be right up there.
'I don't see why not. He knows and understands the game, he's had a great grounding in the game.
'When I was manager of Bournemouth I saw him at Gillingham and recommended him to top sides. They didn't take any notice and he ended up going to Norwich and moved to Manchester United and you can't have a better manager than Sir Alex Ferguson, so he's had a good grounding.
'He's done it all as a player and now as a manager and there's no reason why he can't go on to be an England manager. And I like him as a guy, he's a terrific guy as well.'
Meanwhile, Tottenham joined the debut on naming rights when Paul Barber, the club's executive director, confirmed that the club are bidding for a stadium sponsor.
Chelsea revealed that they are to replace the name of Stamford Bridge with a company brand, and Spurs, who are to build a new stadium adjacent to White Hart Lane, will rename the new arena using a corporate name.
And Barber believes the attraction of a new, state-of-the art stadium, will prove an attraction to would be sponsors.
'It I think the key thing is that word 'new',' he said. 'It is a new stadium as opposed to White Hart Lane and that's the fundamental difference to what Newcastle have done and what Chelsea are planning.
'There's a balancing act; it's great those stadiums exist already and that a sponsor can come straight in and name them tomorrow. But of course they've got with that the associated heritage and history of St James' Park and Stamford Bridge to contend with in the name.
'We have left the path clear for a sponsor to come in from day one, just as Arsenal did with the Emirates, so there are two very different scenarios.'