The Bantams climbed into sixth place in League One with victory over Sheffield United at the weekend, but Parkinson has admitted that he has not set the club a target.
"We feel we've got a decent squad, but who knows at this stage how we're going to fair? We've got a good spirit in the camp, we've got some good quality players, we've got a good mentality, but we've come into a new division and we're still in the very early stages," he told PA.
"We're still in the relative unknown. There's a whole batch of teams this season who you see challenging at the top end. Last year when you looked at this division it was difficult to pick out, but this year there's a list of teams who potentially could be up there, Wolves obviously, Bristol City, Sheffield United, Peterborough, Preston.
"There's some big clubs this season, it's a great division to be involved in and we're going to enjoy the challenge."
Leyton Orient currently top League One with 12 points.