The discovery came when divers were sent down to search inside the USS John S McCain, now berthed at Singapore's Changi naval base.
The collision with a Liberian-flagged ship happened before dawn on Monday as the US vessel made a routine port call.
The US has since ordered a worldwide "operational pause" of its navy fleet.
It was the fourth crash involving a US Navy ship in a year, and the second in the past two months.
The collision ripped open the port side of the US vessel, flooding parts of the ship including crew compartments.
Admiral Scott Swift, commander of the US Pacific Fleet, said divers "were able to locate some remains in those sealed compartments during their search today".
The navy was also examining whether a body found by the Malaysian navy was one of the missing sailors, he said.
Ships, equipment and aircraft from the American, Indonesian, Malaysian and Singapore navies have been involved in the search for the missing sailors.
The USS John S McCain was east of Singapore when the collision occurred. It was reported before dawn at 05:24 local time on Monday.
The destroyer sustained damage to her port side, which is the left-hand side of the vessel facing forward. Five sailors were injured, four of whom were medically evacuated to a Singapore hospital.
The tanker it collided with, Alnic MC, sustained damage to a tank near the front of the ship 7m (23ft) above the waterline, but none of its crew were injured and there were no oil spills.
The Alnic MC, carrying oil from Taiwan to Singapore, is currently at the Raffles Reserved Anchorage in Singapore.