The police watchdog is investigating the conduct of several officers over allegations they sent the discriminatory messages over WhatsApp.
The material was said to be misogynistic, racist and homophobic, The Times reported.
As a result, two Met officers and another who used to work at the force, not Couzens, are the subject of a criminal probe by The Independent Office for Police Conduct (IOPC) for improper use of phones.
They, alongside a Norfolk police officer and one from the Civil Nuclear Constabulary and another from the Met, are under investigation over allegations they sent the messages between March and October 2019, and for claims they failed to challenge the messages.
It has since been reported by The Guardian that two of the Met officers are still on duty, while the officers from other forces have been suspended.
The mobile phone messages were discovered during the police investigation into Ms Everard’s murder.
They are among 16 people the IOPC is looking at in several misconduct probes.
The watchdog said will soon decide what further action will be taken against a police constable on probation, who ended up staffing the cordon in the search for Ms Everard, who was investigated for gross misconduct for allegedly sending an inappropriate image over WhatsApp about the case while off-duty.
Two other constables on probation were also investigated over allegations they shared the graphic and failed to challenge it.
The watchdog’s report and conclusions have been passed to the Met.
Findings will be published when a final decision has been made on what action will be taken against another group of officers, from several different forces, amid allegations one shared details of the interview Couzens gave under caution when there was “no policing purpose to do so”, and claims six others failed to challenge this, two of which were accused of joining in the conversation.
The IOPC said criminal or gross misconduct investigations do not necessarily mean that charges or disciplinary proceedings will follow.
Commenting on the investigation, Boris Johnson said “issues” in the police force had to be addressed and suggested recruiting more female officers could make a “fundamental change”.
Speaking with broadcasters he said: “You will have seen this stuff about the officers on the WhatsApp group.
“We’ve got to come down very hard on them.”
He added: “Should we believe in the police?
“Should we trust in the police? Yes I do.”
An investigation into how Couzens sustained head injuries while in custody on March 10 and 12 found they were “self-inflicted” and the correct procedures were followed by the Met.