Swift said the Malaysian navy had reported locating other body and was working to confirm whether it was one of the missing USA sailors.
Seven sailors died in mid-June aboard the USS Fitzgerald when it collided with a Philippine cargo ship off the coast of Japan.
Swift also said that Malaysian authorities, one of three countries involved in the major hunt for the missing sailors who are feared dead, had also found a body.
A U.S. Navy guided-missile destroyer has collided with a merchant ship in waters east of Singapore and the Straits of Malacca.
U.S., Malaysian and Singapore diving crews have been combing the ship in search of remains or survivors. Planes are still searching the surrounding waters, but the new area of focus was a discouraging sign for the missing sailors' loved ones. The impact tore a hole in the warship's waterline, flooding compartments that included a crew sleeping area, the US Navy said. Swift says bodies were discovered but it's premature to say how many or the status of their recovery.
US Defense Secretary James Mattis said on Monday that an extensive investigation was underway to "look at all related accidents, incidents at sea".
Navy officials are now investigating the role that training, manning and other internal fleet processes may have played in the deadly collisions, and have imposed a rare operational pause following the accidents.
Ten US sailors are missing.