The Pompey boss admitted he is thinking of an unbelievable bid to hijack the England superstar's proposed loan switch to AC Milan.
Beckham's planned move to Serie A for two months is the talk of the football world.
The planet's most recognisable footballer is weighing up joining the Blues' UEFA Cup rivals in January from Los Angeles Galaxy.
>>> Braga v Pompey is not live on UK television. So join The News for live minute-by-minute match updates and join in the debate. Click here for more.But Redknapp has admitted he has given serious consideration to making a bid for the 33-year-old which would go down as the coup of all coups.
He confessed it may now be too late with Beckham close to agreeing a deal with the Rossoneri.
Redknapp hasn't given up all hope, however.
He said: 'I haven't made an enquiry for David Beckham – but it has crossed my mind to.
'If he is going to Milan it might be too late now.
>>> Beck off Milan, Harry's lurking!: - Burton's BanterClick here to read the latest post.'But as a player on loan you'd have have to think about it.
'I'd be interested in signing him. I'd take him, for sure.
'Don't tell me he can't create goals for Peter Crouch and Jermain Defoe still.
'He is in great nick still and wants to play football. If he wants to come to the Premier League then fantastic. I'm sure we would not be the only ones up for going for him if he showed interest.
'I might still do it tomorrow – I'm sure his missus would love shopping in Portsmouth instead of Milan!
'He'd be a great signing, absolutely terrific.'
Redknapp's Beckham revelation has overshadowed the build-up to tonight's clash with Braga.
Pompey are without Lassana Diarra (knee), Younes Kaboul (back) and Niko Kranjcar (ankle), who all remained back in England as they recover from injury.
Redknapp targeted a positive start in the group opener.
He said: 'We are in for a tough game. Braga are a good side.
'There aren't going to be any easy games in our group. But we have come here to be positive and try to win.
'The reports I've had on Braga tell me they are a good side with dangerous players.
'They have drawn with Bayern Munich and went to to Bolton last year and got a draw. They are good results and they are a good team.
'We are going to be without Lassana Diarra. We need our best players.
'But we were without him against Stoke and Villa and got good results there.'
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