Wells has been sidelined for the Bantams' last four matches with an ankle problem picked up against Shrewsbury Town last month but could be seen being put through his paces on the pitch before City's away match at Crawley Town last Saturday.
Despite making this progression in his recovery from injury though, Wells wasn't deemed fit enough to play a part in Tuesday's draw at Preston North End.
The popular frontman took part in a training session at City's Apperley Bridge training ground this Thursday but, as he has mentioned several times before, Parkinson says Wells will only be made available for selection when he is in the right shape to justify his place in the team.
Parkinson said: "Nahki has trained today (Thursday) and we'll have a look at him this week to see how he feels after getting back out on the training pitch.
"It will obviously be a boost to have Nahki back in contention but we will not rush him. We looked threatening again against Preston on Tuesday without him.
"We have to make sure we get him back out on the pitch only when he is feeling right and when he is ready."