The physio treating Kanu for a knee injury says the striker could return to training next Monday.
The Nigerian forward has been sidelined since scoring the winner at Ewood Park last month.
He has seen a specialist in France this week and had an injection to help reduce soreness in his knee.
And Pompey physio Gary Sadler says the 31-year-old is improving all the time and could be in contention for the Premier League clash with Wigan on Saturday week.
Wear and tear
"He's got some wear and tear in the knee and the injection is designed to lubricate and provide nutrition to the joint surfaces," Sadler told the club's official website.
"There's a period where you need to allow the nutrition and lubrication to start working, and we don't want to hinder that.
"So what we are aiming to do is give Kanu some time off and then start to push him on Monday so that he has the chance of being involved against Wigan.
"Kanu has a specialist in France he has a lot of faith in. I went out with Kanu and Benjani last week to meet him.
"I think if a player has a lot of faith in somebody and we get to meet them then it's the best thing for the player to be treated by them."
Papa Bouba Diop also hopes to be fit to face Wigan after shaking off a hamstring injury.