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The officers, along with a former Met officer, are the subject of the criminal probe, police watchdog the Independent Office for Police Conduct (IOPC) said.
The three officers are also being investigated for gross misconduct for allegedly sending messages of a discriminatory or inappropriate nature in the Whatsapp group between March and October 2019.
A further Met Police officer, one from the Civil Nuclear Constabulary (CNC) and one from Norfolk Constabulary are also under investigation in the misconduct probe.
The criminal investigation was revealed on Thursday as the IOPC gave an update on its linked investigations following the sentencing of former PC Wayne Couzens.
The IOPC said in a statement: “The mobile phone messages were discovered during the police investigation into Ms Everard’s murder.
“Three of the serving officers are with the MPS, one from the Civil Nuclear Constabulary (CNC) and one from Norfolk Constabulary. The former officer was previously with the MPS.
“They are being investigated for gross misconduct for allegedly sending messages of a discriminatory and/or inappropriate nature, and for allegedly failing to challenge the messages sent by the others.
“Two of the MPS officers and the former MPS officer have also been notified that they are being criminally investigated for improper use of the public electronic communications network under Section 127 of the Communications Act.”
In other updates the IOPC said it 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 image and failed to challenge it. The watchdog's report and conclusions have been passed to the Met.
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.
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The IOPC provided no update into their investigations into police investigations into two earlier sex crime allegations against Couzens.
There is no date yet for when their findings will be published, despite mounting pressure to discover how the Met officer “slipped through the net” before raping and murdering Sarah Everard.
The police watchdog said on Thursday it will aim to conclude investigations into officers’ conduct linked to the Sarah Everard case “as swiftly as possible”.
IOPC regional director Sal Naseem said: “We cannot provide updates for some of our investigations linked to Couzens, which are ongoing, but following today’s sentencing (of Couzens), we will look to bring those matters to a conclusion as swiftly as possible.”
Chief Inspector of Constabulary Sir Tom Winsor confirmed Couzens was known as “the rapist” by other officers at times during his career and the IOPC was investigating what other officers knew about him.
Asked on BBC Radio 4’s The World At One if he was aware of Couzens’s reputation as “the rapist”, Sir Tom said: “Yes, I do know that. And (he) also had allegedly a reputation in terms of drug abuse, extreme pornography and other offences of this kind.”
He also warned that police officers are failing to raise concerns about colleagues who exhibit “damaging or worrying” characteristics.
There appeared to be a “culture of colleague protection” within the service, he said, adding: “The concern that I have is that there is in too many respects and in too many places a culture of colleague protection.
“Forces are not sufficiently spotting and dealing with concerns about behaviours and attitudes when constables are in their probation when they should be thrown out.
“In too many respects, there is evidence of police officers who become aware of damaging or worrying characteristics in police officers of not reporting them, not putting up a warning flag, and that needs to change.”
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