The first year pro has featured in eight matches for City this season but only two of those appearances have come from the start - once in the Johnstone's Paint Trophy and once in the Capital One Cup.
With the arrival of Jon Stead on loan from Huddersfield Town further boosting the Bantams' attacking options, Parkinson feels the time is now right to get McBurnie a run of football elsewhere.
Parkinson said: "We feel the time is right to get Oli McBurnie out on loan.
"We want to get him out there and playing some first team football. We feel the time is right.
"Whether it is at non-league level or somewhere else, he needs to move away and get a run of games.
"To do that though, we needed another striker in and we have that now with Jon (Stead)."