UN investigators urged the United States last month to close the Guantanamo camp, saying it violated a host of human rights including a ban on torture and the right to fair trial.
"It is important that the EU (plays) its part in convincing the US," Manfred Nowak, the UN's rapporteur on torture and one of the investigators into Guantanamo, told reporters in Brussels on Thursday.
Many of the 500 inmates in the prison at the US naval base in Cuba have been held for four years without trial. The prisoners were mainly detained in Afghanistan.
Angela Merkel, the German Chancellor, is the only European leader to have publicly called on the United States to close the camp. The European Parliament made the same call last month.
Nowak said it was time for the EU to raise the issue with the United States and "quiet diplomacy" might be the most efficient way forward.
EU countries could take some of the detainees and try them before their own courts, he said.
Nowak also voiced concerns about European countries extraditing terrorist suspects to countries with a record of systematic torture such as Egypt or Syria.
He said Britain and Sweden were pushing other countries in the 46-countries Council of Europe to allow extraditions of suspected terrorists if the country to which they were sent gave assurances that they would not be tortured.
But such assurances could not be monitored, he warned.