McBurnie, 18, signed a professional contact with the football club last season and made nine appearances for City during the campaign.
The young forward, who received his first Scotland Under 19s cap back in November, had featured in ten games for Phil Parkinson's side this season.
Fellow first year professional, Niall Heaton, is set to leave the Coral Windows Stadium permanently after agreeing a deal with Conference club Alfreton Town.
Heaton signed his first professional contract with City this summer but he has yet to feature in any of Parkinson's teams this campaign so far.