Nafea Faa Ipoipo (When Will You Marry?) was painted in 1892 and had been owned by a Swiss collector.
Unconfirmed reports suggest the painting was sold to a museum in Qatar.
Qatar paid the previous highest price for a painting, a work by Paul Cezanne which sold for $259 million.
Before its sale, the Gauguin artwork had been owned by Rudolf Staechelin, a collector from Basel.
For decades it had been on loan to the Kunstmuseum Basel but Rudolf Staechelin decided to sell the painting after a disagreement with the museum, the New York Times reported.
Rudolf Staechelin told the New York Times he would not divulge the identity of the buyer.
It was not immediately clear where the sale had taken place.
However the paper, which first reported the sale, quoted sources saying the painting had been sold to Qatari buyers.
Officials in Qatar have not yet confirmed the purchase.
The sheikhdom’s royal family has in recent years spent vast amounts of money on Western art.
Sheikh Saud bin Mohammed Al-Thani, a former minister of culture who died last year, lavished more than $1 billion of the country’s money on artworks.
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