The striker has been engaged in lengthy negotiations regarding his Fratton Park future, as speculation mounted over a possible move away from the south coast after the high-profile signings of David Nugent and John Utaka.
But Redknapp revealed chief executive Peter Storrie has finally hammered out a contract with the Nigerian, who scored 12 goals last season, and is confident Kanu will put pen to paper when the Pompey chief returns from the Asia Trophy in Hong Kong.
"We've been speaking to him for several weeks and Peter Storrie has managed to thrash out a deal with his agent and with Kanu, and I'm sure he's going to sign a new contract next week," said Redknapp.
"He'll sign for one year with an option for a second if he plays 20 games. That's the deal Peter's put to his people and they've accepted that."
Despite six players arriving at Fratton Park this summer, Redknapp revealed he is still keen to add at least one more new face to his squad with prolific Sevilla striker Fredi Kanoute a possible target.
And with the number nine shirt still available, there is a good chance any new recruit will be to bolster the forward line regardless of whether a deal for Kanoute comes off.
"Fredi was a player we watched a couple of times at the end of the season," said Redknapp.
"He played with me when he was at West Ham so he's a player I know very well, but whether there's anything to be done there I'm not sure.
"We're still looking. I'm happy with the squad but if I could make maybe one more signing, I would do.
"But if it doesn't happen we'll push on with what we've got.
"We've made enquiries about two players and one of them might come off.
"I've got good strikers but the number nine shirt is still available and we'll have to wait and see who fills that shirt."
Redknapp also dismissed talk Sol Campbell could be on his way out of the club.
The veteran defender played a crucial role in Pompey's fine start to last season as they did not concede a goal in their first six Premier League games and eventually finished just outside the European places, thanks largely to a much-improved backline.
And Redknapp insisted the former England international was going nowhere despite the inevitable summer speculation to the contrary.
"We want to keep our best players and Sol Campbell is certainly a top player for us," said Redknapp.
"There's lots of speculation but he signed a two-year contract and we expect him to be here for two years.
"There's a year left on his contract so we'll see how he goes, he's a major part of our plans and we need him here.
"To maintain progress you need to keep your best players."