According to British newspaper the Guardian, permission for two US lawyers to see the five detainees at the US naval camp next Monday is being seen as a key move in trying to get them freed.
The US granted the visits after its Supreme Court ruled the base in Cuba was covered by American law despite the Bush administration claiming it was not, the report adds.
The Guardian said two British nationals, Muazzam Begg and Firoz Abbasi, have been suffering mental health problems during their imprisonment.
Both have been held in isolation for up to a year, with Begg having been detained in a windowless room, it added.
He was reportedly denied human contact after he started talking to guards and is monitored by a remote controlled camera.
During four days of visits next week, US lawyers are also expected to see British national Martin Mubanga, and two other London residents whom the Foreign Office refuses to represent, the Guardian said.
They are Bashir al-Rawi, an Iraqi national who had lived in Britain for 20 years, and Jamil al-Banna, a Jordanian refugee.
Lawyer Gitanjali Gutierrez, who will see Begg and Abbasi over four days, said the visit would help prepare their habeas corpus petitions in the US courts which she hoped would see them freed.
Gutierrez said the Pentagon was trying to apply conditions on the visit that she regarded as unacceptable, the paper said.
Four residents of Britain and four
of its citizens are incarcerated
These include reading the notes made by the lawyers of their meetings with the prisoners and monitoring any mail between the two.
Gutierrez reportedly said negotiations were continuing for the Pentagon to drop these conditions. It has already been agreed that the meetings will not be monitored.
A total of four British nationals and four British residents are among the 585 remaining detainees at Guantanamo Bay, according to the Guardian.
Five British prisoners were released in March from the camp on the eastern tip of Cuba where Washington is holding foreigners whom it suspects of involvement in the al-Qaida network and Afghanistan's deposed Taliban.
Three of those - Asif Iqbal, Ruhal Ahmad and Shafiq Rasul, all from Tipton in northwest England - said in a dossier published in New York in August that they had been abused by their US captors.
Their 115-page report detailed incidents of sexual and religious humiliation, as well as brutal interrogation methods that induced false confessions.
Their claims followed similar allegations of mistreatment from Spanish and French former prisoners.