Cullen hasn't trained for the last couple of days after reporting himself ill, and it seems probable that City will not risk the 19 year-old if he is not fully fit.
Fellow loanee midfielder Lee Evans had also been suffering with illness during the week but he is expected to be available for the weekend.
Parkinson said: "Lee is fine - he is back in training today (Friday).
"Josh has had a sickness bug recently so he is looking very doubtful at the moment.
"We have options within the squad to cope should Josh miss out though. Whoever we pick, we are confident they can come in and do a job."
After missing Tuesday's win over Southend United due to the birth of his first child, Rory McArdle - a former Rochdale player - is back in contention for a place against one of his old clubs.
Parkinson continued: "It has obviously been an amazing few days for Rory and we are all delighted for him.
"The baby is fit and healthy which is the main thing, and Liz (Rory's wife) is also doing well.
"He is back in training now and he understandably has a spring in his step.
"We now have to decide which combination to play on Saturday between Rory, Reece (Burke) and Nathan (Clarke) - it is good to have that competition for places."