Chelsea defender Branislav Ivanovic is understood to have spoken to Surrey Police about the incident at the club's training ground in Cobham.
Press Association reports that a complaint was made to Merseyside Police which was passed on to their Surrey colleagues, who wanted to ascertain whether he had sustained any injury.
That was found not to be the case and Ivanovic told police he did not want to press charges.
Luis Suarez failed to "fully appreciate the gravity and seriousness" of his bite on Branislav Ivanovic, an FA report concluded.
The FA says it intends to punish Suarez more than the usual three games. Well why is it? He didn't hurt anyone. Ivanovic is not in plaster.
Liverpool had a real chance to steal the moral high ground. Among fans I heard irritation that Suarez had stained the club’s name again.