Hanson was substituted just before the hour mark during Wednesday's Emirates FA Cup replay win over Aldershot Town.
Meredith has come back from international duty with an irritation of an old foot injury, while Burke is still feeling some discomfort from a knee problem picked up in training on Monday.
Checks on Hanson's ankle issue this Thursday have revealed the striker has suffered some ligament damage.
Although the injury isn't too serious, City's medical staff will have to let the problem settle down before the striker can be allowed to return to training.
Parkinson: "We don't believe it is anything major but Matt (Barrass, Head Physio) wants to look again at James before we decide what we want to do."
Lee Evans will be back in contention for the trip to Glanford Park after returning from a spell away with Wales Under 21s, playing in both of their recent home games against Armenia and Romania.