Guy Morin, the mayor of Basel, acknowledged news of the sale of the Gauguin and bemoaned its loss. On Tuesday, The Baer Faxt, an art world insiders’ newsletter, said Qatar was rumored to be the buyer of the Gauguin at $300 million, which would exceed the more than $250 million that Qatar reportedly paid for Paul Cézanne’s “The Card Players” in 2011.

Todd Levin, a New York art adviser, said of the Gauguin, “I heard that this painting was in play late last year.” He added, “The price quoted to me at that time was in the high $200 millions, close to $300 million.”

In recent years the Qatar royal family and the museums authority have been reported to be expansive buyers of trophy quality Western modern and contemporary art by Mark Rothko, Damien Hirst and Cézanne. In a move that jolted Basel as news of the sale trickled out, Mr. Staechelin said that his family’s trust was ending its loan to the Kunstmuseum as a result of a dispute with the local canton. He said that he was searching for a top museum to accept the Staechelin collection — which also includes works by van Gogh, Picasso and Pissarro — on loan, without a lending fee, with a promise to integrate the pieces into permanent exhibitions.

The works were amassed by his grandfather, a Swiss merchant also named Rudolf Staechelin, who befriended artists and made most of his purchases during and after World War I. Later, the elder Mr. Staechelin advised the Kunstmuseum, which accepted the loan of his collection after his death in 1946.

The grandson said that the works had never been hung in his family’s home because they were too precious and that he saw them in a museum along with everyone else. He has decided to sell, he said, because it is the time in his life to diversify his assets. “In a way it’s sad,” he said, “but on the other hand, it’s a fact of life. Private collections are like private persons. They don’t live forever.”