Kanu is expected to return to action next week.
The veteran striker has been sidelined with a bad back so far during the pre-season tour of America.
That has prevented the striker from joining in with a full training session.
He also sat out Thursday’s 2-2 draw against a Charleston Battery XI in the opening friendly.
But Steve Cotterill believes Kanu could be back to stake a claim to feature against Charleston Battery on Wednesday, July 27.
The Blues manager said: ‘Kanu may join in with the lads in the early part of next week.
‘He’s got a bit of a bad back at the moment, which is his problem.
‘But he’s getting a lot better.
‘He has been out on the training field now for the past couple of days so we are hoping for the early part of next week.’
Meanwhile, Liam Lawrence came safely through Thursday’s match with no reaction to his calf problem.
Pompey’s skipper played the opening 45 minutes in what was his first game this pre-season.
But Cotterill is wary about unleashing the midfielder for the full duration against Charleston Battery next week.
He added: ‘I thought Liam played very well and I was really happy with him.
‘But we don’t want any setbacks, we just have to play the game as we see it at the time.
‘On Thursday, he was always going to play only 45 minutes.
‘He’s obviously a very good player and one of the better players at the football club, but at the end of the day it was more important he played 45 minutes rather than the result.’