McMahon will have a scan on his hip injury this Thursday to see if he has any chance of featuring against the Lions at the Coral Windows Stadium.
The Millwall fixture is one of two games for the Bantams in just three days over the Easter period, with Parkinson's men also set to travel to Crewe Alexandra on Monday.
With City missing players for both matches due to international call-ups on top of the need to possibly freshen things up between games, Parkinson knows he will be making changes to his side this weekend regardless of whether McMahon is passed fit or not.
Parkinson confirmed: "McMahon is having a scan on his hip today (Thursday).
"Hopefully it is not too bad but we won't know for certain until we get the results of the scan in the afternoon.
"We have to contend with these two games (in quick succession). We have players who have not played recently who are back in the frame.
"Some of them have been unfortunate not to play but they will get an opportunity.
"We have players like Josh Morris, Billy Knott, Paul Anderson and Filipe Morais who are back in the mix and looking for their chance.
"Jamie (Proctor) is a great example of someone who was out of the side but then took his chance with both hands when he did get an opportunity.
"Tom Thorpe has also come into the building this week and he is really determined to make his mark with us.
"I'm sure he will get an opportunity over these next two games.
"Whoever comes in, I'm sure the fans will give them every bit of support."