Aviation experts who have studied photos of the debris found on Reunion say it does resemble a flaperon - a moving part of the wing surface - from a Boeing 777.
The wife of the in-flight supervisor for the missing MH370 plane, Jacquita Gonzales, told the BBC that she was "torn" by the news.
"A part of me hopes that it is [MH370] so that I could have some closure and bury my husband properly but the other part of me says 'no, no, no' because there is still hope," she told the BBC by phone.
Reunion, a French territory, is about 600km (370 miles) east of Madagascar.
The search efforts for MH370, led by Australia, are focused on a broad expanse of the southern Indian Ocean - some 6,000km to the east of Reunion.