Saddam was hanged in the early hours of December 30.
Nasir al-Badri, Al Jazeera's correspondent in London, reported that Abdel-Rahman has applied for political asylum and that the British Home Office was considering his application.
"We contacted the British Home Office to make sure whether he and his family have applied for asylum but they refused to comment, saying they did not comment on personal or private cases", al-Badri said.
"But the accredited sources we first talked to were 100 per cent sure they have examined some papers and documents Abdel-Rahman has presented besides an application for residence in Britain", he said.
Besides sending Saddam to the gallows, Abdel-Rahman had also sentenced two other top Saddam aides to death in the same trial.
The two were Saddam's half brother and former intelligence chief, Barzan Ibrahim al-Tikriti, and Awad Hamed al-Bandar, former head of Iraq's Revolutionary Court.
They were found guilty along with Saddam of involvement in the Dujail killings in 1982.