Officers from the Surrey force, on behalf of their north-west colleagues, attended Chelsea's Cobham training ground on Sunday night to speak to the Serbia international.
However, Ivanovic did not report any physical injury and told police he did not want to pursue the matter.
"Merseyside Police can confirm that, following an incident at the Liverpool v Chelsea game yesterday, officers have spoken to Branislav Ivanovic in person," a statement from Merseyside Police read.
"He had no apparent physical injuries and did not wish to make a complaint.
"This is now a matter for the Football Association."
Football's governing body is currently reviewing the incident, which happened in the 2-2 draw at Anfield.
The club have fined Suarez, who asked for the money to be donated to the Hillsborough Families Support Group, but have no plans to sell the Uruguay international in the wake of the controversy.
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