Three officials, speaking to Reuters news agency on the condition of anonymity, said the recommendations were part of discussions on a draft plan by the US military.
While talks are at an early stage, no decision has yet been made, the officials noted.
The Pentagon said it would be “inappropriate” and premature to comment on what will happen with the weapons.
“Planning is ongoing, and focused on executing a deliberate and controlled withdrawal of forces while taking all measures possible to ensure our troops’ safety,” said Commander Sean Robertson, a Pentagon spokesperson.
It is unclear what the Pentagon will ultimately recommend to the White House in the coming days. But the final decision will be made by President Donald Trump, who ordered the withdrawal of about 2,000 US troops from Syria earlier this month.
The move prompted Jim Mattis, the US defence secretary, to resign.
The US officials said Trump’s announcement has upset American commanders, who view his decision as a betrayal to the northern-based Kurdish fighters.
The People’s Protection Units (YPG), which embodies the Syrian Democratic Forces (SDF), has been the backbone of an alliance that has spearheaded the US-backed fight against the Islamic State of Iraq and the Levant group (ISIL, also known as ISIS) in Syria.
They are perceived as a “terrorist” group by Turkey, which has vowed to launch an operation in Syria targeting areas under the control of YPG fighters.
‘Fight isn’t over’
The US told the YPG that they would be armed by Washington until the fight against ISIL was over, one of the officials said.
“The fight isn’t over. We can’t simply start asking for the weapons back,” he said.
The proposal to leave US-supplied weapons with the YPG, which could include anti-tank missiles, armoured vehicles and mortars, would reassure Kurdish allies that they were not being abandoned.
But Turkey wants Washington to take the weapons back, so the commanders’ recommendation, if confirmed, could complicate Trump’s plan to allow Turkey to finish off the fight against ISIL inside Syria.
The Pentagon keeps records of the weapons it has supplied to the YPG and their chain of custody. But the US officials said it would be nearly impossible to locate all of the equipment.
“How are we going to get them back and who is going to take them back?” one of the officials said.
The debate over whether to leave weapons with the YPG coincides with Trump’s NSA John Bolton’s visit to Turkey and Israel next week for talks on Syria.
In May 2017, the US began distributing arms and equipment to the YPG for an offensive against Raqqa, the de facto capital of the self-proclaimed ISIL caliphate.
Washington told Ankara that it would take back the weapons after the defeat of ISIL, which has lost all but a few slivers of territory in northeastern Syria.
“The idea that we’d be able to recover them is asinine. So we leave them where they are,” said a US official.
A person familiar with the discussions of the US withdrawal plan said the White House and Turkish President Recep Tayyip Erdogan would oppose the proposal to allow the YPG to keep its US-supplied weapons.
The recommendation “is a rejection of Trump’s policy to withdraw from Syria”, said the person, who requested anonymity.
Turkey has said weapons supplied to the YPG have in the past ended up in the hands of Kurdish separatists, and described any weapon given to the fighters as a threat to Turkey’s security.
Meanwhile, the Kurds have welcomed a Syrian government advance in the city of Manbij in the northeast of Aleppo Governorate, a pragmatic shift in alliances that will dash their aspirations for autonomy but could help them cut their losses.
“We invite the Syrian government forces… to assert control over the areas our forces have withdrawn from, particularly in Manbij, and to protect these areas against a Turkish invasion,” the YPG said in a statement.