US Defence Secretary Jim Mattis is expected to raise the issue during a meeting in Rome this week with other members of the coalition that is fighting the Islamic State group in Iraq and Syria.
The SDF is currently holding thousands of IS detainees, including hundreds of foreign fighters from a number of nations. The issue became more prominent in recent days, after the announcement that the SDF had captured two notorious British members of an Islamic State cell who were commonly dubbed the Beatles and were known for beheading hostages.
US officials have said putting the two in the notorious Guantanamo Bay detention facility is not an option. UK leaders have suggested remain doubtful that they want two men two men to return to Britain.
London raised El Shafee Elsheikh and Alexanda Amon Kotey fought with IS and were captured in early January.
"We're working with the coalition on foreign fighter detainees, and generally expect these detainees to return to their country of origin for disposition," said Kathryn Wheelbarger, the principal deputy assistant defence secretary for international security affairs.
"Defence ministers have the obligation and the opportunity to really explain to their other ministers or their other Cabinet officials just the importance to the mission, to the campaign, to make sure that there's an answer to this problem."
Speaking to reporters travelling with Mattis to Europe, Wheelbarger said the key goal is to keep the fighters off the battlefield and unable to travel to other cities.
"The capacity problem is very real," Wheelbarger said, noting that at one point the SDF was capturing as many as 40 militants a day.
"Success in the campaign means you get more people off the battlefield... These facilities are eventually going to be full."
French journalist Nicolas Henin, who was held by the men and their comrades for 10 months, said he wants justice, and that the men should be tried in Britain, not shipped to Guantanamo Bay, because revenge will just breed more violence.
"What I'm looking for is justice and Guantanamo is a denial of justice," he said.
Wheelbarger said the detainee problem is just one of the issues the defence ministers will discuss during the meeting.
The Islamic State group has been largely defeated in Iraq and is near destruction in Syria, where pockets of insurgents still operate along the Euphrates River, near the Iraq border and in other scattered locations. As a result, the coalition is shifting from an emphasis on combat operations to stabilisation.
"There are numerous questions about what's next," said Mattis.
He said that will include ensuring that explosive devices are found and eliminated, getting schools re-opened and making sure clean water is available.
The Syrian conflict began when the Baath regime, in power since 1963 and led by President Bashar al-Assad, responded with military force to peaceful protests demanding democratic reforms during the Arab Spring wave of uprisings, triggering an armed rebellion fuelled by mass defections from the Syrian army.
According to independent monitors, hundreds of thousands of civilians have been killed in the war, mostly by the regime and its powerful allies, and millions have been displaced both inside and outside of Syria. The brutal tactics pursued mainly by the regime, which have included the use of chemical weapons, sieges, mass executions and torture against civilians have led to war crimes investigations.