The court has now been asked to rule specifically on whether a federal court can order the release of the prisoners in the US.
Susan Baker Manning, a lawyer for the group, told the AFP news agency on Monday that she was "hopeful" the court would grant a hearing in autumn this year.
The US has tried unsuccessfully for several years to arrange the transfer of the
Uighurs to a third country, saying the men face possible persecution if they return to China.
Albania accepted five Uighur detainees in 2006 but has said it will not take others, partly due to fears of diplomatic repercussions from China.
The group originally comprised 17 men; however; three of the Uighurs have said they do not want the case to continue.
The men were captured mainly in Pakistan and Afghanistan during the US-led war in Afghanistan following the September 11, 2001, attacks.
The Uighurs are Turkic-speaking Muslims who say they have long been repressed by the Chinese government.
China in turn says that Uighur nationalists are leading an separatist movement in the country's Xinjiang province.