With Saturday's opening league encounter in mind, Jones and Davies were not risked for the Bantams' trip to Meadow Lane four days ago due to slight hamstring and thigh problems respectively.
Jones has now returned to full training ahead of this weekend's scheduled journey south and Davies is believed to be very close to joining him.
Parkinson said: "They were only niggly injuries but if you try and rush people back you can sometimes make things a bit more serious.
"We decided not to push things with those two last week with this Saturday in mind.
"As much as we wanted them to be in contention for the Notts County match, you have to be careful."
Should the pair indeed make it onto the bus for Gillingham this weekend, they will both face stiff competition to get into Parkinson's side for the Gills match.
Will Atkinson and Gary Jones blended together nicely in central midfield at Notts County despite the former's relative lack of experience in that position, while Rory McArdle and Luke Oliver expertly led a City defence to an extra time clean sheet against the League 1 Magpies.
Team-mate Matt Duke, who himself is expected to face a battle with fellow shot-stopper Jon McLaughlin for the 'keeper's spot at Gillingham, believes there's nothing wrong with players being kept on their toes when it comes to securing themselves a starting berth.
“We know that if we're in the team and performing well then hopefully the manager will have no reason not to select you," said Duke.
“But, equally, if you don’t perform then there are players, like Jonny (McLaughlin) for me, who can come in and take your place. That isn’t just the case for me, but for all the lads all over the pitch.
“Not just in the goalkeeping department, we have players throughout the squad who can come in and take someone’s place within the team.
“It’s great competition for places, and we all know that we have to keep performing to our best to keep our places. That can only be a good thing for the manager and the team as a whole."