Although the defender has been hampered with a slight ankle problem recently, McArdle is set to play a part in Northern Ireland's friendly fixture in Turkey this Friday evening.
The 26 year-old is scheduled back in England late Saturday afternoon following the game in Adana, leaving Parkinson with a potentially tricky decision on his hands.
Parkinson is understandably keen to have McArdle available for selection, but he knows he must factor in the defender's efforts during the Turkey friendly and the travelling involved as well before making a final call.
Parkinson said: "How much game-time he (Rory) gets Friday night will have a say in what we do with him in terms of Sunday.
"Rory is a very fit lad and I imagine he would be very keen to play against Coventry. He has already told us as much, and he's also had the opportunity to rest his ankle up a bit.
"I suppose we will just have to see how things go and make a call Saturday evening or Sunday."
The decision on whether to start with McArdle or not for Sunday's clash with Coventry isn't the only one in Parkinson's mind at this present time though.
The Bantams boss is still undecided on which two out of Raffaele De Vita, Garry Thompson, Mark Yeates and Kyel Reid will start on the wings, while Parkinson also has to mull over what striking options he wants on the bench.
Oliver McBurnie is in contention once again to be named among the Bantams' substitutes following his debut appearance off the bench at Rotherham United last weekend. Fellow forwards Caleb Folan and Andy Gray gave Parkinson food for thought, however, by scoring in a private friendly win at Mansfield Town this Tuesday.
Parkinson continued: "We are not going to name the team to the lads this week until the last minute probably.
"This is partly due to Rory's situation, but also because we want to take in training and see who we think is really ready for this match on Sunday.
"I was really pleased with the reserves at Mansfield this week. Caleb and Andy got the goals and the defenders - Matt Taylor, Luke Oliver and Carl McHugh - all put in really good performances.
"They are really pushing for a place in the team.
"What I said after the Rotherham game about wanting to see competition for places and people pressuring the players already in the side, I can sense that happening around the training ground this week.
"Ollie is in there competing as well. He was away with Scotland Under 18s earlier this week at a training camp but he has come back to the training ground today and trained.
"He is another one we have to factor in when looking at our options from the bench. Caleb and Andy have scored this week, while Ollie came off the bench last week.
"Whatever happens with Ollie this week though, he is definitely in the melting pot and in the thinking for selection on merit."