Mr Saito, the former chairman of the Daishowa Paper Company in Tokyo, told friends that the painting should be cremated with him when he died so his children would avoid colossal death duties. He died three years ago from a stroke.
The missing work is one of two portraits by Van Gogh of Paul-Ferdinand Gachet, a doctor who treated him at the end of his life in 1890.
The Metropolitan Museum of Art in New York had hoped to include the work in a current exhibition of Van Gogh portraits. But its curators were unable to locate it. It was then that stories of Mr Saito's unorthodox cremation request came to light. Mr Saito apparently suggested that the Van Gogh and a Renoir, purchased at the same sale for $78.1m, should be burnt with his body.
Nobody has given up hope that the work may have changed hands and that the new owner has chosen to remain anonymous. There is no indication, however, that it has been seen since Mr Saito's death. He apparently made the cremation remark after being hit in 1990 with a tax bill of $24m.
A spokesman for the Metropolitan Museum of Art said: "We tried to borrow it for our Dr Gachet show, but we couldn't find the owner. We don't even know who sold it."
It is not even clear that Mr Saito enjoyed the Van Gogh much when he was alive. It is reported that he looked at it once before ordering it to be stashed in a warehouse.