Bellfield has applied for permission to marry a woman while he is serving two whole life orders for murdering Marsha McDonnell, Amelie Delagrange and Milly Dowler.
He added: “Milly never got to see her wedding day. It cannot be right that he gets to have his.”
The Sun said he is engaged to a female visitor and got down on one knee to propose in front of prison staff at HMP Frankland in County Durham.
A Ministry of Justice spokesman said: “An application has been received and is being considered in the usual way.”
However, it is understood that Bellfield’s application is still being processed and is not at any further advanced stage.
The 53-year-old killer would need the permission of the prison governor to marry at the category A men’s prison.
Bellfield was given a whole life term for murdering Ms McDonnell, 19, in 2003, and murdering Ms Delagrange, 22, and attempting to murder Kate Sheedy, 18, in 2004.
He was already serving this sentence when he went on trial for killing schoolgirl Milly, who was snatched from the street walking from school to her home in Walton-on-Thames, Surrey, in March 2002.
Bellfield was found guilty of abducting and killing the 13-year-old following a trial at the Old Bailey in 2011.