Evergreen Portsmouth striker Kanu is on course to earn himself a new contract at the end of the season.
Kanu scored his third goal in six Premier League appearances in the 1-0 win at Blackburn to give Pompey their first away victory since Boxing Day.
Another 14 more games from the Nigerian, along with a few more goals, should be enough to see Kanu, 31, putting pen to paper again next summer for the Fratton Park club.
Dismissing suggestions he would have been happy to offload the striker during the summer, Redknapp said: 'I always wanted to keep him, but he was looking at two years (on his contract).
'So I said he could have a year and if he played 20 games, I saw that as a fair deal for him. It was then just a matter of convincing him, so I said to him, 'If you don't play 20 games then you are not worth another year.'
'Then I added, 'But you will play 20 games because you are still good enough'. In the end he was okay with that, and that's the deal he got. He has since played in every game bar one.'
Kanu was asked to lead the line on his own at Ewood Park, and he did so superbly, earning his just reward in the 25th minute.
After being denied by two stunning Brad Friedel saves in a matter of seconds just a minute previously, Kanu showed strength, touch and composure to net the winner and thrill Redknapp.
'You can imagine what he was like when he was 20 because he is a great talent, a special talent,' said Redknapp. 'You watch him in training and he can do things with the ball that are just amazing.
'But then you don't play for AC Milan, Ajax and Arsenal if you are not a good player, and he has been a top, top player.'
Kanu even shrugged off the threat of a knee injury sustained in training on Saturday to start the game.
'He went out for the kickabout before kick-off and the physio said that if he played we might lose him for a couple of weeks,' added Redknapp. 'But he said he would give it a go, so he went back out again and it's good for us that he did.'
Redknapp will put his 'terrific squad' theory firmly to the test tomorrow.
Redknapp will again ring the changes for his side's Carling Cup third-round tie with Burnley at Turf Moor.
The wily Pompey boss made nine for the 3-0 victory over Leeds in the previous round from the side that lost 1-0 at Chelsea three days previously.
Redknapp is likely to make as many again for the game against the Clarets, especially as it follows hot on the heels of a 1-0 win at Blackburn yesterday.
The likes of Matt Taylor, David Nugent, Noe Pamarot and Benjani Mwaruwari - on the bench at Ewood Park - can expect to start, as well as Pedro Mendes, Richard Hughes and Arnold Mvuemba.
'You look at us now and we are a strong-looking team,' remarked Redknapp. 'You look at the back four and I honestly wouldn't swap them for any other in the country, and I genuinely mean that.
'We've two great centre halves in (Sylvain) Distin and (Sol) Campbell, then we've (Hermann) Hreidarsson and (Glenn) Johnson. It's a very strong-looking back four, while the goalkeeper (David James) is the best in the business.
'We're also now strong in midfield. Papa (Bouba) Diop and (Sulley) Muntari give us power there, so we look a good team, and we've a terrific squad. Pedro Mendes wasn't even on the bench yesterday - I went with two forwards along with Matty Taylor and Noe Pamarot - and yet he is a terrific player.
'So in going to Burnley it gives me a chance to give the likes of Pedro a game, and I'll change things around because they are good enough to play. It's not as if they're poor players. We've some good players who didn't play against Blackburn.
'It's a chance for them to show themselves, but then I've enough belief in them and I know they can do the job.'
Redknapp is hoping his team can now gain some momentum after their first away victory since Boxing Day, secured courtesy of Kanu's 25th-minute winner.
That was enough to elevate Pompey to 11th, a respectable position considering they have already played Manchester United, Liverpool, Arsenal and Chelsea this season.
'The only setback we've had this year was against Arsenal when we were turned over in the first half,' reflected Redknapp. 'They ripped us up with some fantastic play, but they're special when they play these days.
'They beat Tottenham 3-1 at White Hart Lane, and they beat Seville 3-0 and then Derby 5-0. They're on another level. The football they are playing at the moment is fantastic and they are going to smack most teams. It's hard to live with them.
'So apart from one dodgy half, we've been terrific all season. We have more than held our own. But make no mistake Burnley are going well and Steve (Cotterill) has done a terrific job, so it will be a tough game.'