Both Connell and Gray weren't selected in City's squad for last weekend's home fixture with Wolverhampton Wanderers and neither are expected to travel to the game at Crewe Alexandra this Saturday either.
After scoring nine goals in his debut season for City last campaign, Connell has yet to begin a game for the Bantams in League 1. His only starting appearance this season so far came in the Capital One Cup First Round tie at Huddersfield Town back in August.
Hampered by a broken arm picked up at the start of pre-season, Gray has yet to feature in any first-team games for City this campaign despite being on the bench four times.
The duo's current situation now mirrors that of midfielder Ricky Ravenhill, who has also been given permission by Parkinson to leave on loan should the right move crop up.
Parkinson said: "If a club comes in for them, and we think it is the right move for all parties, then we feel we are in a position to give up at least one of them.
"We'll see if anything happens and take it from there.
"Both players have been great professionals since coming into the football club and we want to be fair to them"