The Christian singer was the subject of a two-year South Yorkshire Police investigation which centred on sexual assault accusations dating between 1958 and 1983 made by four men.
He was never arrested or charged and is now suing the BBC for filming a police raid on his Berkshire home.
At the beginning of August an application under the victims' right to review scheme was lodged by an accuser - challenging the decision by the CPS not to pursue a case against Sir Cliff.
The process allows an alleged victim, within three months of the original decision, to call for it to be reviewed.
It is understood a lawyer will look at the evidence before deciding to uphold or overturn the original decision made by the CPS.
A spokesman for the CPS confirmed they have received an application under the victims' right to review scheme over the decision made in relation to the star adding it is "ongoing".
Some have called for people accused of crimes to remain anonymous until charge, citing the Sir Cliff case as an example of an innocent person's reputation being damaged by false accusations.
Others say it's vital people accused of crimes are named in order to encourage other potential victims and witnesses to come forward.
Sir Cliff said in June when the case against him was dropped: "I have always maintained my innocence, co-operated fully with the investigation, and cannot understand why it has taken so long to get to this point.
"Nevertheless, I am obviously thrilled that the vile accusations and the resulting investigation have finally been brought to a close."
