Bassong headed in a last-minute equaliser to give Norwich a 1-1 draw at Everton in the Premier League on Saturday and was reportedly subjected to abuse on the micro-blogging website after the game.
Norwich chief executive David McNally confirmed that the club were aware of the reports.
"For those asking last night (Saturday), we will be following up with the police regarding the racist comments reported after the game," he wrote on Twitter.
He later added: "Not relevant which team they (people accused of abuse) support. Don't accept racism from anyone and so these comments will be reported to the police."
Norwich to report 'racial abuse' of Bassong
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