A Swansea City supporter was released on bail on Sunday after being arrested for allegedly making racist gestures during his club's 4-3 loss at home to Norwich in the Premier League on Saturday.
The 23-year-old fan reportedly gesticulated at Cameroon international Bassong as Norwich celebrated their fourth goal.
Norwich say that the three other allegations concern racist messages sent to Bassong on Twitter following the match against Swansea and the 1-1 draw at Everton last month.
"Norwich City regrets to confirm four separate cases involving actual or alleged racist abuse aimed at our defender Sebastien Bassong have been reported to police in the last two weeks," said a club statement.
Police from South Wales and Norfolk are investigating the claims.