Tony McMahon, who finished last season on loan at City, completed a permanent move to the Coral Windows Stadium last Friday to become the Bantams' third summer capture following the arrivals of Steven Davies and Josh Morris earlier in the week.
All three signings came during City's first week back in training, with Parkinson eyeing up more new players as the Bantams continue their pre-season preparations ahead of their first friendly of the summer on Saturday (11 July 2015) at Farsley Celtic.
Parkinson said: "We've signed three players so far and we're still looking.
"We've had meetings with other players and there are a couple of offers out there. We are just waiting to hear back.
"We've just still got over a month to go until the first game though. We've only just had the first week of pre-season so you can never tell how long these things will take."