George Brinkley alleges the Sheffield United striker left him in fear of his life by twice stamping on his shin during a pitch invasion.
McBurnie is a Rangers fan and could make a move north of the border in the summer transfer window.
Bramall Lane officials are investigating after a video appeared to show McBurnie in a confrontation on the street.
Sheff Utd forward Oli McBurnie will miss the rest of the campaign after sustaining a foot fracture against Arsenal.
The Sheffield United striker has twice been at the centre of those accusations in the past 14 months.
McBurnie was spotted supporting his former club Swansea in the away end during their 0-0 draw at Cardiff.
The goal celebration is the delectable icing on the football cake. The contrast between McBurnie and Lacazette was stark.
The 23-year-old is accused of driving over the limit in Leeds in the early hours of Friday, West Yorkshire Police said.
A video of the clip appeared on social media and has attracted criticism from fans of the Tartan Army.
Oli McBurnie “fits the profile of our transfer policy this season”. For £20m, Sheffield United would hope so.