The Bantams travel to fifth-placed Peterborough this weekend but striker James Hanson is a doubt for the contest due to a tight calf. Italian winger Raffaele De Vita also has a slight issue with his thigh.
Young striker Oliver McBurnie is another player being monitored after taking a whack in Tuesday's F.A Youth Cup tie against Millwall.
Fellow forward Caleb Folan is likely to be sidelined for the Peterborough match with the same hamstring problem that has been bothering the striker for the last couple of weeks.
With the Peterborough game marking the start of City's run of Christmas/New Year fixtures, Parkinson has told supporters not to expect him to take any unnecessary risks when it comes to the fitness of his players.
Parkinson said: "We have a few injuries about - nothing major - just a couple of things picked up this week in training which have been frustrating.
"Hanse (James Hanson) and (Raffaele) De Vita will need to be assessed beforehand, while Caleb is still not quite right with his hamstring.
"Oliver McBurnie also took a whack in Tuesday's (F.A Youth Cup) game as well. As I say, none of them are major injuries, but the heavy grounds of earlier in the week certainly haven't helped.
"We just have to make sure that we don't put anyone out there who is not ready because we don't want to lose them for any longer."
Regardless of the current fitness situation for the likes of Hanson though, Parkinson admits that changes will be made to his starting line up over the course of the traditional hectic Christmas schedule.
Starting with City's trip to Peterborough this Saturday, the Bantams play four times in just twelve days during the festive period.
Parkinson has acknowledged that some players will be rested and rotated during the club's next four matches in an attempt to keep his side fresh as the games come thick and fast.
The Bantams boss added: "We are treating Saturday as the start of the festive period of fixtures for us.
"For all of our supporters, it is important that they are aware that changes to the side will be made throughout these games.
"It would be unrealistic to expect the same players to go through the Christmas period and play every one of the games. There are players who haven't been playing recently who will be getting a game.
"I always feel that the team that has the ability to freshen things up over this period and still keep the side strong is usually the one that comes out with the right results.
"From our point of view, we have to make sure we get our planning right in terms of match preparation and team selection.
"There will be some players who have played all the games previously but might miss a match over this festive period, or at least half a game. We will be mixing it around.
"This will definitely be a busy period for us but it is one the whole group is looking forward to.
"Personally, I love being involved in football over the Christmas period. The games at this time of year always seem to have that extra bit of excitement and that extra bit of atmosphere.
"As footballers, sacrifices have to be made around this time of year but I know we have a group of players here who are willing to do what it takes to give us the best chance of performing to our maximum over all four of these games."
This Saturday's match-up with Darren Ferguson's Peterborough side will see two of the hottest strikers in League 1 go head-to-head at London Road.
Peterborough's Britt Assombalonga has sixteen goals in total so far this season while City's own Nahki Wells has fifteen goals to his name, making the pair the top two forwards in the division.
As a result, Parkinson expects there to be a number of interested on-lookers at the game waiting to see how the pair get on - himself being one of them.
Parkinson added: "There will be the two top goalscorers in the division out on the pitch on Saturday.
"That itself will be interesting to see because I am sure the directors' box will be packed with scouts watching on. People will look at the game and see it as a good opportunity to see two players at once who have both been talked about a lot recently.
"They'll be both out in the same environment, on the same pitch, in the same weather, and we'll see which one does the best.
"The good thing from our point of view is that Nahki usually rises to these sort of challenges. We talk to him about pushing himself to be the best in the division. At the moment he is doing that well, but he has to keep doing it."
The full video with Bantams boss Phil Parkinson on Bantams Player can be viewed by clicking HERE.