Lowery, who died aged six in July 2017, suffered from a rare form of cancer which spreads rapidly across the body. He became known nationally as he accompanied the team in taking to the pitch before matches.
British media reports said that a 14-year-old boy had handed himself in to West Midlands Police, who launched an investigation after footage circulated on social media appearing to show an individual in the Coventry section displaying an image of Lowery during Sunderland's 3-1 defeat on Saturday.
"Coventry City FC is aware of footage circulating on social media in connection with an incident during our Premier League fixture against Sunderland," the club said in a statement.
"The club does not tolerate offensive behaviour and will liaise with the relevant authorities to determine the appropriate course of action."
Lowery, Bradley's mother, issued a statement on Sunday through the Bradley Lowery Foundation, which supports children and families affected by serious illness.
"As his (Bradley's) mam (sic), this breaks my heart. Behind that photo is a little boy who was loved beyond measure," she said.
"I hope the club takes appropriate action and the young lad's family help him understand how hurtful his actions were."
Reuters has contacted Sunderland and West Midlands Police for comment.