The 33-year-old marketing executive vanished as she walked home in Clapham, south London, on 3 March. Her body was found a week later in Kent woodland.
The Met’s Directorate of Professional Standards is set to question staff who accessed files on the case.
Doing so “without a purpose” could be a criminal offence, the force said.
The Sun first reported that more than 30 Met Police officers and staff were under investigation.
A Met spokeswoman said officers and staff needed to have access to computer records, but were only permitted to review specific information.
She said that accessing records without a legitimate reason could amount to a breach of professional standards or even be a criminal offence.
“Officers from the Met’s Directorate of Professional Standards are in the process of contacting those officers and staff who accessed records relating to the investigation into the abduction and murder of Sarah Everard to ensure that each access was for a legitimate policing purpose,” the spokeswoman said.
“Once all the responses have been received, a decision will be taken as to whether any further action is required.”
PC Wayne Couzens, 48, from Deal in Kent, is accused of Ms Everard’s kidnap and murder.
He is due to appear at the Old Bailey for a plea hearing on 9 July.
At a previous hearing, a provisional trial date was set for 25 October.