Steve Cotterill believes Dave Kitson is homing in on a return against Barnsley.
The striker has missed the past five matches through, firstly, illness and then a torn stomach muscle.
In his absence, Benjani has been given a run in the central-striking role.
But Pompey continue to find goals hard to come by and remain short of options in forward positions.
Kitson, who scored the winner against Reading earlier this season, has yet to return to training following his injury.
That means he will not feature in the friendly against FC Rostov tomorrow night.
The Blues’ next Championship fixture is the visit of Barnsley on Saturday, October 15.
That Fratton Park clash is to be shown live on Sky Sports in a 5.20pm kick-off.
Pompey desperately need to improve their fire power.
And Cotterill is hopeful to have Kitson back for the clash with the Tykes.
He said: ‘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.
‘He’s not even back in training at the moment so tomorrow’s game is too soon for him. He won’t be featuring in that.
‘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.’
Kitson’s last appearance was in the 1-1 draw with Cardiff in August.
Young striker Marko Futacs has found himself on the bench in his absence, making three appearances.
Kitson netted eight goals in 37 appearances last season.