McArdle took a nasty blow to the face last Friday following an accidental clash of heads during a training session at the club's Apperley Bridge training base.
The incident left him with severe swelling around his left eye and raised fears that the defender could have fractured his cheekbone.
X-rays on the injury fortunately proved otherwise, although McArdle was still deemed unfit to play in Saturday's home match with Crewe Alexandra.
Three days on from the training ground injury and the swelling around McArdle's eye has gone down significantly, meaning Parkinson has refused to rule out the possibility of a return at Carlisle for the Northern Ireland international.
Parkinson said: "Thankfully, he is looking a lot better now.
"If you look at him now compared to Friday, you'd hardly believe it because it looked a real mess when he'd first done it. It definitely looks a lot better today (Monday).
"He is one in particular that we are giving an extra twenty-four hours to before we finally complete the team for Tuesday night."