McArdle will be forced to sit out the festive fixture after picking up his fifth booking of the season at Peterborough United on Saturday.
Parkinson has three main defensive options to choose from as a replacement - Carl McHugh, Luke Oliver and Matt Taylor - and the Bantams boss is confident in the ability of each of them to do a job for the team against the Millers if needed.
Parkinson said: "All three of them are currently vying for that position. We have to look to pick the one who we feel is right for this occasion. We will be making changes over the Christmas period depending on games and opponents, and we will look to pick the best player for the Rotherham game on Boxing Day.
"They have all trained well today (Monday) and I am absolutely sure that any one of the three lads will do themselves justice if selected on Thursday."
Saturday's goalscorer at Peterborough, Andy Gray, is currently nursing a dead leg picked up during the match at the weekend and will need to be assessed before Boxing Day.
Fellow forward James Hanson, who sat out the Peterborough trip with a calf problem, missed training having been troubled overnight with a stomach bug on Sunday, meaning City medical staff were unable to assess the progress of his injury this Monday.