Parkinson has been talking with a number of players in the recent days and weeks, with similar discussions planned with potential new recruits ahead of City's return to pre-season training next Monday.
While Aaron Mclean, Matthew Dolan, Jason Kennedy, Andy Halliday, Mark Yeates and Matt Urwin have all left the club, Parkinson is hopeful that he will be able to add to his group by the first week of the Bantams' pre-season preparations.
Parkinson said: "We are looking to strengthen the squad we have here, not weaken it, and plans are in place to do just that.
"Talks are on-going - we are working on a number of things.
"We return for training next week and we hope to have brought some new additions to the squad during the first couple of days. If not then, hopefully by the end of that week."