In fact, after years of being in “dire straits,” Mr. Boulware said the museum was finally starting to right itself.

In recent months, it received $11.6 million from the Federal Emergency Management Agency to repair the damage caused by Sandy. The museum’s budget is $2.5 million — about half of what Mr. Boulware said was needed to thrive, but an improvement from recent years.

The museum is also close to completing an $11 million renovation of the Wavertree, the other tall-mast sailing ship that has long called the South Street Seaport home. One of the last surviving wrought-iron sailing ships in the world, the Wavertree has been undergoing repairs at a shipyard on Staten Island. If all goes according to plan, it will return just as the Peking departs.

Mr. Boulware, sitting on the worn deck of the Peking, said that instead of having two ships in failing condition, the museum would have one in both top condition and with a firm connection to New York City.

While the Peking may have established a presence for itself in New York, its sailing history has little to do with the city.

Built by the German company F. Laeisz, it was the last of a generation of sailing ships, constructed just as steam-powered vessels were on the rise.