The Sun has reported that the serial killer got down on one knee to propose to the woman, who began writing to him two years ago before she became a regular visitor.
Prisons minister Victoria Atkins is reported to have ordered an immediate review of the request, calling it 'absolutely appalling’.
Bellfield was found guilty in 2008 of the murders of Marsha McDonnell and Amélie Delagrange, and the attempted murder of Kate Sheedy, and was sentenced to life imprisonment. In June 2011 he was also found guilty of the murder of Milly Dowler.
The 53-year-old previously worked as a car clamper at Chichester Gate.