Johnny Begue, who found the “flaperon” part while cleaning a beach last July, told AFP he handed over the new suspected object to police immediately after finding it last Thursday.
He said he was out jogging by the sea shore when he found the object measuring about 40 by 20cm, which had a blue mark on the surface and was grey underneath.
Begue said it was of the same lightweight “honeycomb” construction as the flaperon piece.
The flaperon he found remains the only piece of debris identified with certainty as having come from the flight.
Begue said he has been combing the island’s shores ever since.
Police have not contacted Begue since he handed over the new object on Thursday, he said.
The Gendarmerie Brigade for Air Transport – the police unit which investigated the first find – could not immediately be reached by AFP for comment.
MH370, a Boeing 777, was carrying 239 passengers and crew when it vanished on March 8, 2014, on an overnight flight from Kuala Lumpur to Beijing.
Begue’s reported find came three days after an American amateur investigator found suspected MH370 debris in Mozambique, some 2,100km west of Reunion.
That object, which is about a metre long, has been sent to Australia for expert analysis.
Malaysian Transport Minister Liow Tiong Lai said last Wednesday that initial information indicated a “high possibility” it came from a Boeing 777.
An international team of investigators probing the loss of flight MH370 will issue a statement on Tuesday, the second anniversary of the plane’s disappearance.
The unprecedented Australian-led hunt for wreckage from the flight is expected to finish its high-tech scanning of a designated swathe of seafloor in the remote Indian Ocean by July.
Australian, Malaysian and Chinese authorities plan to end the search – projected to cost up to $130- million (R19,96-billion) – at that point if no compelling new leads emerge.