The USS Bataan was to be in the area "in a matter of days," said the official, who spoke on condition of anonymity.
The move was described as "precautionary" in case conditions in Libya, where militia battles have plunged the country into anarchy, worsen and require the embassy's evacuation.
The State Department said last week that the embassy in Tripoli was operating normally despite an offensive launched against Islamist militias by a dissident general, Khalifa Haftar.
The United States also has available 250 marines, seven tilt-rotor Osprey aircraft and three refuelling aircraft in Sigonella, Italy.
The precautions come amid ongoing controversy over a September 2012 attack on the US consulate in Benghazi in which four Americans, including ambassador Christopher Stevens, were killed.