The alleged offence took place during Saturday’s match between Killie and Hearts at Tynecastle.
The hosts won the game 1-0 but afterwards Magennis made a complaint that he’d been a victim of racially aggravated abuse from a supporter.
The man is said to have been sitting in section E of the Wheatfield Stand. He’s described as white, stocky, dark receding hair and in his mid-40s. He was also said to have been wearing dark glasses and a dark jacket, which may have had red lining.
Police are asking for anyone with information to come forward.
THE SCOTSMAN ON SOCIAL MEDIA