Reader is thought to be being treated at Queen Elizabeth Hospital for prostate cancer, although a spokesman for refused to comment due to patient confidentiality.
In January, a photograph of Reader surrounded by police officers being wheeled into an ambulance outside London's Kings College Hospital was published in The Sun.
A member of the public who took the picture said: "He looked like any other sick, old man in a wheelchair but was surrounded by police. Some had what looked like machine guns."
Video:Will The Police Find 'Basil'?
Dubbed the "Master" by his co-conspirators, the pensioner had been instrumental in planning the Hatton Garden heist, although he withdrew from the conspiracy when the group first struggled to get into the vault on the night of 2 April, 2015.
He was the oldest man involved in the raid and he pleaded guilty to conspiracy to commit burglary.
In 1983, Reader was jailed for eight years for his part in the £26m Brink's Mat gold bullion armed robbery at a Heathrow Airport warehouse.