Clarke missed the goalless draw at Walsall last Saturday and Tuesday's win over Crawley Town after straining his hamstring in training just under a week ago.
The influential attacker has started light running again following the injury but it is believed this Saturday's encounter with Peterborough United at the Coral Windows Stadium may still come too soon for him.
Nevertheless though, Parkinson is confident it won't be too long before City fans get to see Clarke back in the claret and amber again.
Parkinson said: "Billy's injury is just a minor one. He will be close soon again.
"He is an intelligent player and he has made a good start for us but we don't want to force him back. It is nice to be in a position where we don't have to rush him back too soon."