Abu Ghaith, the former spokesman of the Al-Qaeda network, was seized last month at a luxury hotel in Ankara after a tip-off from CIA and was held there by the police despite a US request for his extradition.
Turkish authorities deported Abu Ghaith to Jordan on March 1 to be sent back to Kuwait but he was seized by CIA agents in Jordan and taken to the United States, the Hurriyet newspaper said.
His deportation coincided with a visit by US Secretary of State John Kerry to Ankara as part of a regional tour, it added.
The Turkish foreign ministry declined to comment on the report while the US embassy in Ankara told AFP: "We're aware of the reports."
Ankara considers Abu Ghaith a "stateless" person as he was stripped of his Kuwaiti nationality after appearing in videos defending the September 11, 2001 attacks on the United States and threatening further violence.
The United States wanted him extradited over his alleged connection to the attacks.
He appeared in a propaganda video in the aftermath of 9/11, standing beside bin Laden, who was killed in May 2011 in Pakistan in a covert US operation.
Abu Ghaith was detained in Turkey after he allegedly entered the country illegally from Iran.
He was freed by an Ankara court because he did not commit any crime on Turkish soil and local media claimed Turkey had hesitated to extradite him to the United States fearing it could become a target of Al-Qaeda.