The Serbian stopper, who suffered "no apparent physical injuries", was interviewed by police on Sunday evening but does not want to take the matter through legal channels.
Suarez has publicly apologized and has been fined by the Reds for his "inexcusable behavior", while any potential punishment from the Football Association is still pending.
"Merseyside Police can confirm that following an incident at the Liverpool v Chelsea game yesterday (Sunday, 21 April 2013) officers have spoken to Branislav Ivanovic in person," the force said in a statement. "He had no apparent physical injuries and did not wish to make a complaint.
"This is now a matter for the Football Association."
Liverpool have fined Suarez an unspecified amount for his actions, while the Professional Footballers' Association has offered him anger management counseling.
Despite calls from many pundits that the Reds should sell their striker, managing director Ian Ayre has stated that the issue has no bearing on Suarez's Anfield future.