Bassong, who made 34 appearances for Newcastle United, is believed to be the subject of racist abuse on Twitter.
The Cameroon defender headed a late equaliser to earn the Canaries a 1-1 draw at Everton in the Premier League on Saturday.
Norwich are aware of the comments and McNally tweeted on Sunday: "For those asking last night, we will be following up with the police regarding the racist comments reported after the game.
"Not relevant which team they support. Don't accept racism from anyone and so these comments will be reported to the police."