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The Jamaican Defence Force said the plane went down about 14 miles (22km) north-east of Port Antonio.
The US had earlier scrambled two F-15 fighter jets when the plane failed to respond to air traffic control.
The two people known to be on board have been named as Larry Glazer, a property developer from Rochester, New York, and his wife Jane.
The couple were both licensed pilots.
Major Basil Jarrett of the Jamaican Defence Force told reporters that an oil slick had been spotted off the coast but there was no sign yet of any wreckage.
He said search and rescue teams were scouring the waters for possible survivors.
The North American Aerospace Defence Command (Norad) was alerted to the unresponsive plane about an hour into its flight and sent two fighter jets to monitor it.The plane, a Socata TBM-700 built in 2014, took off from Rochester at 08:26 (12:26 GMT) en route to Naples, Florida.