Malcolm Millman, 58, absconded during a day visit to a monastery in St Margarets, Great Gaddesden, near Hemel Hempstead, at about 2pm on Saturday.
Millman is under the care of Chadwick Lodge, a secure facility in Chadwick Drive, Eaglestone.
He is white, of large build, bald with thinning brown hair on the sides, and brown eyes.
Millman was last seen wearing a brown jacket, purple jumper, grey tracksuit bottoms and blue and white trainers.
He was also carrying a walking stick. Millman is also known by the following names: Richard Simon Barber, Michael Geoffrey Newman and Raymond Pilkington.
Thames Valley Police believes that Millman travelled from Hemel Hempstead to London on Saturday. It is possible that Millman travelled to London by train; the nearest railway station to the monastery is Hemel Hempstead.
Officers believe that Millman took a train to Leeds from London and that he was in the city between 6am and 8am on Sunday.
The last sighting of Millman is at Manchester Airport where he was captured on CCTV just before 1pm on Monday. Police do not believe Millman has access to a passport.
Millman has links to Kent, specifically Canterbury.
Thames Valley Police took the investigative lead from Hertfordshire Police yesterday.
Supt Olly Wright said: “We are continuing our appeal for information to trace absconder Malcolm Millman who failed to return to a medium security facility in Milton Keynes.
“Millman was convicted of rape in 1996 and was due to serve twelve years, however he was working towards his full release while under the care at Chadwick Lodge. Based on Millman’s previous convictions, including rape, we believe he is a potential risk to the public. If any members of the public see Millman do not approach him, instead call 999.
“Our renewed appeal today focuses on Malcolm Millman’s movements since leaving the monastery in St Margarets, Great Gaddesden, Hemel Hempstead, at about 2pm on Saturday. From there, we believe he travelled to London, possibly catching a train at Hemel Hemstead railway station.
“From London, we believe Millman took a train to Leeds and that he was in the city between 6am and 8am on Sunday.
“The last sighting of Millman is at Manchester Airport where he was captured on CCTV just before 1pm on Monday. We thank Greater Manchester Police for their hard work to obtain these images and we continue to work closely with GMP, as well as Hertfordshire Constabulary and Kent Police.
“I would like to stress that we do not believe Millman has access to a passport, however he may have taken a train or a bus from Manchester Airport to another location within the city or another part of the United Kingdom.
“If you think you saw Millman as he travelled from Hemel Hempstead to London, Leeds and Manchester then please call police on 101. Further, if you are reading this and have any information whatsoever about Millman’s whereabouts then please contact police immediately.
“If you don’t feel comfortable speak directly to the police then you can contact the independent charity Crimestoppers anonymously on 0800 555 111 or online at www.crimestoppers-uk.org. No personal details are taken, information is not traced or recorded and you will not go to court.”