Three rambling apartments at 907 Fifth Avenue were put up for sale this year by the estate of Huguette Clark, a copper heiress known for her reclusiveness and her multimillion-dollar doll collection. Just two of these apartments take up the entire eighth floor of the building, with more than 20 rooms, a 100-foot expanse overlooking Central Park and a combined asking price of $31 million.

Despite the huge price tag, a buyer was found in a few weeks, a man who hoped to buy two apartments and join them as one: Sheik Hamad bin Jassim bin Jabr al-Thani, the prime minister and foreign minister of Qatar and a member of that country’s royal family.

This week, Mr. Thani’s offer was rejected by the co-op board, people with knowledge of the deal said. According to those people, all of whom spoke on the condition of anonymity, the board said the application was rejected because members did not want the apartments to be combined.

And that is where agreement ends.

One person with knowledge of the process said the board indicated early on that combining the apartments would not be a problem, so they were offered to buyers separately or together.

“I think it’s sad to make everybody in different parts of the world put together a board package only to have it be declined,” that person said, adding that the board should have made its reservations about combinations clear months ago. On the seventh floor, three apartments have been listed for sale only as a combination, at an asking price of $25 million, since January.

A resident of 907 Fifth Avenue with knowledge of the board’s decision-making process said, however, that the concern was the nuisance that Mr. Thani’s large entourage and security detail would cause for his neighbors. “He could have been from England, he could have been from France, it was an issue of privacy in the building,” the resident said. Had Mr. Thani been allowed to buy the two apartments, he could have waved to the emir of Qatar, Sheik Hamad bin Khalifa al-Thani, who owns two mansions just across the street, at No. 7 and No. 9 East 72nd Street. His visits, the resident of the building said, cause snarled traffic and increased security.

Mrs. Clark was as quiet a neighbor as one could ever hope to have — because she was never home. For her last two decades, she chose to live in hospitals, even when in good health, leaving her three apartments and Connecticut mansion largely empty, but for her enormous collection of dolls. She died last year at the age of 104.

The Qatari Embassy in Washington did not respond to a request seeking comment about the rejection of Mr. Thani, which was reported by msnbc.com on Monday. The listing agents on the eighth-floor apartments, Mary Rutherfurd and Leslie Coleman of Brown Harris Stevens, declined to comment, as well.

Whatever the board’s reservations were, it is unlikely that the sheik’s ability to finance the purchase was one of them. A member of the ruling elite of Qatar, a small, oil-rich nation in the Persian Gulf, Mr. Thani owns toys like a 437-foot yacht called the Al Mirqab, which can accommodate 60 crew members and 60 guests, and features a helicopter landing pad, according to CharterWorld.com. This, it seems, was not enough for this New York City co-op board, a breed that is infamous for being finicky and mysterious.

“They can reject you for any reason, or for no reason at all,” Steven R. Wagner, a real estate lawyer in New York City, said of co-op boards. The only requirement of a board, Mr. Wagner continued, is that its decision not be discriminatory.

The deal for Mrs. Clark’s third apartment, a four-bedroom on the top floor that had been listed for $24 million, seemed more assured on Tuesday. But any future for a combined eighth-floor dwelling appeared to have sailed away.

“Who needs 23 rooms?” said the resident with knowledge of the board’s decision-making. “Think about it — it would have to be a huge family, or maybe an entertainer. We don’t know, but we’d rather not find out.”