Marcel Seip, Rob Kozluk, Luke Dean and Lee Bullock are all out of contract this summer and will not be offered fresh terms.
Parkinson has also told Guy Branston, Steve Williams, Dean Overson, Andrew Burns, Dominic Rowe and Darren Stephenson that they are free to find another club.
But out-of-contract trio Luke Oliver, Simon Ramsden and David Syers have each been offered new deals for next season.
The Bantams will also assess the progress of Matt Fry following groin surgery before deciding whether he gets a new contract, while Mark Stewart has agreed to settle up the remainder of his deal.
Second-year apprentice Adam Baker has already been handed an extension.