Wayne Couzens was handed a whole-life tariff in September after kidnapping, raping and murdering the 33-year-old.
The Metropolitan Police firearms officer used his warrant card and handcuffs to snatch the marketing executive off the street, using Covid lockdown rules to make a false arrest.
The 48-year-old had been planning for at least a month before abducting Ms Everard as she walked home from a friend’s house in Clapham, south London, on the evening of March 3.
A Court of Appeal official said on Wednesday: “An application (for permission to mount an appeal against sentence) has been lodged.”
Passing sentence at the Old Bailey, Lord Justice Fulford said the case in which a serving officer abused his position was so exceptional that it warranted a whole life order, meaning Couzens will never be freed.
It was the first time the sentence had been imposed for a single murder of an adult not committed in the course of a terror attack.
The judge said: “The misuse of a police officer’s role such as occurred in this case in order to kidnap, rape and murder a lone victim is of equal seriousness as a murder for the purpose of advancing a political, religious or ideological cause.”
After the sentencing, Ms Everard’s devastated family said that, while nothing could bring her back, knowing Couzens “will be imprisoned forever brings some relief”.
Earlier this month, Reading terrorist Khairi Saadallah lost a Court of Appeal challenge against his whole-life sentence for the murders of three men, following a hearing at the Royal Courts of Justice.