The Lebanese minister of interior, Nuhaq El Mashnouq, told a local newspaper website that "we located the area of the Cypriot plane wreckage 100 km from the Lebanese coast".
Cypriot media said wreckage from the plane was spotted some 40 nautical miles from Larnaca, on Cyprus's southeast coast.
The Cessna plane disappeared while en route to Beirut. The Cypriot authorities initially deployed a helicopter to search for it while placing other emergency services on standby, police told AFP.
Reports in Beirut said two people, a Lebanese pilot and a Cypriot, were on a training flight.
Air traffic controllers had tried to reach it by radio on numerous occasions, but received no answer.