Kitson has been sidelined for the last five matches, firstly through illness and then a stomach muscle injury.
But boss Steve Cotterill told The News: "Kits should be there or thereabouts for the Barnsley game.
"He has torn a muscle in his side and is in a bit of pain so that is keeping him out at the moment.
"The time frame we are looking at is at the end of the international break, so Barnsley could be the match to see him back."
Pompey play a friendly against Russian side FC Rostov at Fratton Park on Wednesday night to raise money for the families of the victims of the recent air crash in Yaroslavl which killed 44 people, including almost the entire Lokomotiv Yaroslavl ice hockey team.