The Football Association have yet to make an official comment on the incident which occurred during Liverpool's 2-2 draw with Chelsea.
Suarez bit Ivanovic midway through the second half, and he has already issued an apology and Liverpool have condemned the incident.
Now police have become involved after members of the public made contact with the Merseyside Police.
The North West force made contact with their counterparts in Surrey, who visited Ivanovic on Sunday evening - however, the Chelsea defender does not wish to press charges.
Merseyside Police said in a statement: "Following an incident at the Liverpool v Chelsea game yesterday officers have spoken to Branislav Ivanovic in person.
"He had no apparent physical injuries and did not wish to make a complaint."