US Secretary of Defense James Mattis and Joseph Dunford, chairman of the Joint Chiefs of Staff, have not devised an alternate plan, it added.
According to the newspaper, the Obama administration had for years relied on Turkey to send troops or Syrian rebels into Raqqa, but President Recep Tayyip Erdogan focused on fighting Syrian Kurds, which it sees as a greater threat than Daesh.
Central Command commander Gen. Joseph Votel finally asked for authorization to back the Kurds in the fall of 2016, but US administration officials delayed making a decision amid fears it would alienate Ankara.
Three weeks before Trump's January 20 inauguration, Votel and Dunford formally requested armored vehicles, anti-tank weapons, machine guns and mine-clearing equipment for the Kurds and stressed that delaying the delivery could drag the Raqqa operation out for another year.
US-supplied armored vehicles were delivered to Syrian fighters on Tuesday, but Col. John Dorrian said they were transferred to the Syrian Arab Coalition, not the SDF. Another of the SDF's Kurdish components, the Popular Defense Units (YPG) also denied receiving arms from the US-led coalition.