Parkinson has snapped up four players so far this summer - Steven Davies, Josh Morris, Tony McMahon and Luke James - but the City chief knows he still needs more recruits in place before the season-opener at Swindon Town in early August.
He said: "We are building slowly.
"There is still a lot of work to be done but we are getting there.
"All managers would like their squad to already be in place at this stage of the season but sometimes that isn't possible.
"We are working on several players to bring into the squad and hopefully the squad will continue to get stronger."