City officials have been trying to create more places where New Yorkers can ride their bikes safely, but finding secure places to park them is an enduring problem.

Now, a few business executives have dreamed up a private-sector solution: the city’s first bikes-only parking lot, complete with attendant. Already, they have cleared the high hurdle of finding available space in Midtown, on West 33rd Street between Eighth and Ninth Avenues.

All they need is a corporation willing to pay as much as $200,000 a year to sponsor the idea.

“We’re really looking for a big number to build something quite spectacular,” said Daniel A. Biederman, president of the 34th Street Partnership. “We want this to be the premier bike parking facility in the country.”

Stonehenge Management, a developer, has offered a 2,600-square-foot lot next to an apartment building it owns on the north side of 33rd Street, Mr. Biederman said.