The Foreign Office in London would not confirm the reports but said negotiations were ongoing.
A spokesman said: "We are not going to speculate or comment on where the discussions that we are having with the Americans have got to.
"We have had detailed discussions with the Americans, taking forward the requests that the foreign secretary and the home secretary made earlier this year for the five to be released.
"We considered the circumstances of each case with the United States and we are in contact with the families and the legal representatives of the five.
"It is a complex issue and we are not prepared to give a step-by-step account of where this process is. Whilst the discussions are ongoing we are not going to make further comment."
In August, David Miliband, the UK foreign minister, requested that the five residents be returned, reversing London's previous stance of refusing to get involved in the cases of residents without British nationality.
Amnesty International, the UK human rights organisation, welcomed the development.
Neil Durkin, a spokesman for the group, said: "After years of detention without charge or trial in harsh conditions at Guantanamo's isolated military prison, reports that three men are set to be returned to the UK are extremely welcome.
"We've always said that Guantanamo is a travesty of justice and that detainees should either be given proper trials or released to safe countries.
"We will now be seeking to establish why Shaker Aamer is expected to go to Saudi Arabia, why Binyam Mohamed is apparently not set for return, and why another former UK resident, Ahmed Belbacha, has not been mentioned in these reports."
All British nationals detained in the camp were released by January 2005.