The two 6,325-square-foot units will ask just over $40 million each, according to the project’s developers.

By Katherine Clarke

Updated Aug. 22, 2019 12:18 pm ET

A pair of penthouses in an under-construction tower on New York’s Upper West Side are slated to go on the market for roughly $40 million apiece, according to the developers.

At 668 feet, the building, located at 200 Amsterdam Avenue a couple blocks from Lincoln Center, will be the tallest in the neighborhood. While that height gives the penthouses panoramic views of Central Park, the Hudson River and the Manhattan skyline, it has also generated controversy. Planning and preservationist groups challenged the project for several years, arguing it is inconsistent with local zoning regulations. City regulators upheld the developers’ right to build the tower in June, and in July, preservationists filed a lawsuit appealing the decision again.

A spokeswoman for the Municipal Arts Society, one of the advocacy groups opposing the building, said they believe there is precedent for removing some height from a building, even after the construction is completed. In a statement, a spokesman for the project called the appeal “baseless” and said the developers are “confident this latest appeal will again be rejected.”

The two penthouses—the priciest and grandest of the 10 in the project—are 6,325 square feet each.

The lower penthouse comprises the 49th and 50th floors, with four bedrooms and 651 square feet of exterior space, while the upper penthouse spans the 51st and 52nd floors, the highest in the building, and has four bedrooms and 283 square feet of exterior space, the developers said. Both units have stone fireplaces, wet bars, double height staircases and private elevators. CetraRuddy, the firm known for Chelsea’s Walker Tower building, designed all the interiors in the project, which is slated to have entry galleries with marble floors and brushed nickel inlays, white oak floors and marble kitchens.

Building amenities include a spa with a 75-foot heated pool, a meditation room, a fitness center, a Pilates and yoga studio, a golf simulator, a private dining room, a soundproof music rehearsal room, a library and a communal terrace. Residents also get a complimentary yearlong membership at the Lincoln Center for the Performing Arts. The building has a total of 112 apartments, ranging from one to five bedrooms; prices start at $2.625 million for a one-bedroom. Sales of the units launch in September.

Despite a recent bump in transactions motivated by the pending imposition of New York’s mansion tax, Manhattan’s high-end condo market has been generally sluggish in 2019, thanks in part to an over supply of new luxury condos. There are currently more than 50 penthouse listings priced at $20 million or more on the market in Manhattan, according to StreetEasy.

Steven Pozycki, chief executive of SJP Properties, the developer, said he believes the project is insulated from some of the oversupply concerns thanks to its location on the Upper West Side. There is a much higher concentration of new developments in neighborhoods like Chelsea and Midtown. SJP is developing the building in partnership with Mitsui Fudosan America.

“There isn’t one market in New York City, there are numerous submarkets,” said Stephen Kliegerman of Brown Harris Stevens Development Marketing, the real-estate firm handling sales at the building. “The Upper West Side has continually outperformed the market, and there is really very little new product coming on the market there.”

Mr. Kliegerman is working with colleague Jill Mangone on sales.

Write to Katherine Clarke at katherine.clarke@wsj.com