The US has 50 to 60 detainees whom it has been unable to repatriate
European Union countries want to help the US close its Guantanamo Bay prison camp, but will not yet commit to accepting detainees, EU ministers say.
The US has asked other countries to take detainees whom it does not intend to put on trial, and who cannot be sent home for fear they might be mistreated.
The French foreign minister said it was for individual states to decide if they could accept prisoners "case-by-case".
US President Barack Obama has signed an order to shut Guantanamo within a year.
Last month, Portugal told the US that it would offer asylum to some inmates, and urged other EU members to "step forward".
Albania is the only country to have so far accepted Guantanamo detainees on humanitarian grounds, taking in five members of China's Uighur ethnic minority in 2006.
The closure of Guantanamo and the fate of its detainees are being discussed behind closed doors during a meeting of the 27 EU foreign ministers in Brussels.
The EU's foreign policy chief, Javier Solana, said the EU wanted to help on humanitarian grounds, but could not act until the US demonstrated the prisoners did not pose a credible security risk.
"We have not received any demands yet from our American friends," he said. "This is an American problem that they have to solve, but we'll be ready to help if necessary."
"Whenever they ask for help, I think the European answer will be yes," Mr Solana added.
The US has said there are 50 to 60 so-called "hard cases" at Guantanamo, including several Chinese Uighurs, whom it has been unable to repatriate because of human rights concerns. Libyan, Uzbek and Algerian detainees are also said to be at risk.
Ahead of Monday's meeting, Portugal's foreign minister told the Publico newspaper that there were "at least six or seven" countries prepared to take Guantanamo detainees.
"We want a multilateral framework that allows the states to develop initiatives in accordance with their own guidelines," he said.
The UK is so far the only EU country to have taken any former inmates back, and is now focusing on the eventual fate of two former residents who are still being held.
BBC Europe editor Mark Mardell says the Germans, Swedes, Irish and Finns are likely to help, and the Portuguese are pressing for a co-ordinated EU response.
"[Guantanamo's] closure is necessary for the USA, especially if the US wants to restore its credibility in the Middle East and in the Arab world. If Europeans are asked, we should not rule out helping," German Foreign Minister Frank-Walter Steinmeier told the BBC.
At the other end of the scale, the Dutch say Guantanamo was a US mistake they advised against, and that it is up to the US to sort it out, our correspondent says.
"There was nobody very hot about this, that's perfectly true," Czech Foreign Minister Karel Schwarzenberg, whose country holds the EU Presidency, conceded after Monday's meeting.
"Due to the legal situation, we can't give a quick answer," he added.
But our correspondent says that with Mr Obama likely to ask for more troops for Afghanistan and tougher sanctions against Iran, this may be the first of several challenges for European politicians from a US president they want to please.