With initial reports suggested the attacker could be out for up to three weeks, Morais missed last Saturday's victory over Leyton Orient after falling awkwardly on his shoulder early on against Gillingham the week before.
Morais has been back training with the rest of the squad this week, however, after further checks confirmed the injury wasn't as bad as first feared, meaning the former Stevenage man could now be in line for a recall for Sunday's second round tie against the Darts.
Following Morais' return to training, Andy Halliday (illness) and Francois Zoko (hamstring) are currently City's only doubts for the match with the Vanarama Conference side, which kicks off at 2:00pm on Sunday at the Coral Windows Stadium.
Zoko will be able to feature should he shake off his hamstring problem in time after being given permission to play for City in the F.A Cup by parent club Blackpool. Jordan Pickford is still ineligible for the Bantams for this competition, however, meaning Ben Williams is expected to start in goal.
Parkinson said: "He (Filipe Morais) has trained this week. He is looking good and looking fit.
"He is looking fine in terms of the injury so far and it would seem like he will be available for selection for us come Sunday. Given the form Filipe was in prior to his injury, this is obviously good news for us."