The two families are at odds over the John Terry saga earlier this season.
Cole's relatives apparently took to Facebook to gloat about the attack on Ferdinand during Sunday's Manchester derby.
Cole's brother Matthew is reported to have said in a post that seeing the defender hit in the eye had "made his day".
When Ferdinand was hit in the face with the coin as he celebrated his team beating Manchester City 3-2 on Sunday, the Chelsea star's brother Matthew is said to have posted on Facebook: "So happy Rio got hit in the face today when he tried to give it kissing his badge!! Straight in the eye!! Made my day."
According to a report in the Daily Mirror, Cole's mother Sue later added her own comment: "Give the fan that threw it a medal!!"
The Facebook thread was later removed.
Sue Cole denied writing anything online about Ferdinand's injury.
Matthew Cole was unavailable for comment.