The controversial move is apparently being considered amid fears that congress will block plans to transfer many of the Guantanamo detainees to the US.
In a statement on Friday, Mitch McConnell, the senate Republican leader, said that any plans to transfer prisoners to the US or hold them there would only be approved once details of how they would work had been provided.
"Bipartisan majorities of congress and the American people oppose closing Guantanamo without a plan, and several important questions remain unanswered," he said.
McConnell said Obama had demanded the transfers "before the administration even has a place to put the detainees who are housed there, any plan for military commissions, or any articulated plan for indefinite detention".
There are 229 detainees still being held at Guantanamo, but Eric Holder, the US attorney-general, told congress last week that fewer than 25 per cent, or 60, were likely to be charged, while 50 others have been cleared for transfer or release.
However, the fate of the remaining detainees was left unclear.
A Pentagon task force is currently reviewing every case to see which are eligible for transfer or release, which could face trial in civilian courts, which are best suited to some version of a military commission and which are believed too dangerous to free.Classified evidence
Officials say that some of them cannot be prosecuted because evidence against them is either classified, was provided by foreign intelligence services or was obtained through harsh interrogation techniques.
Civil rights advocates have said that any order permitting indefinite detention would see the Obama administration returning to the harmful policies of George Bush, his predecessor.
"Prolonged imprisonment without trial is exactly the Guantanamo system that the president promised to shut down," Shayana Kadidal, a senior attorney for the Centre for Constitutional Rights, said in a statement.
"If the last eight years have taught us anything, it's that executive overreach, left to continue unchecked for many years, has a tendency to harden into precedent."
Obama has pledged to close the Guantanamo bay facility on Cuba by January 31 next year.