Meredith, who broke a bone in his foot back in January, got the all-clear last week to start working outside on the training pitch again and had his first session with Barrass at the club's training ground last Thursday.
The Australian left back hasn't featured for City since the club's fixture at Notts County on New Year's Day.
This latest piece of news is obviously encouraging for the Aussie but it is still unlikely that he will be fit enough to feature at any stage between now and the end of the season.
Bantams boss Phil Parkinson said: "James is the type of player who is itching to get back out there.
"We've been having to rein him back a bit but that's a good thing. We want players who are desperate to get back out there. We also have to be careful though.
"We've got to take it day by day still. It's going to be a long road for him."