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Former President Barack Obama and first lady Michelle are eyeing an apartment in a historic building in Manhattan, multiple sources exclusively tell Page Six.

The Obamas have been looking at 10 Gracie Square on the Upper East Side, situated between East End Avenue and East River Drive and near the mayor’s residence, Gracie Mansion, according to sources who have seen the couple arriving at the building for viewings.

Built in 1930, the white-glove, full-service, pre-war building has 15 floors and 43 apartments. Other notables who have lived there include Gloria Vanderbilt, conductor André Kostelanetz and New Yorker critic Alexander Woollcott.

Plus there’s a gym and an indoor basketball court, which would appeal to the fitness-loving ex-president and first lady. Most importantly, the building has strong security, including an underground drive-in garage, from which they could directly access their apartment without stepping outside.

A duplex apartment at 10 Gracie Square went into contract last week for $10 million, and real estate insiders are speculating that could be the Obamas’ new NYC pad, although this could not be confirmed at press time.

The apartment was designed by architect Daniel Romualdez and features five bedrooms, four baths, a library with a wood-burning fireplace, and views of the East River.

The Obamas could easily afford it, given reports that the bidding to the rights for their joint book deal had skyrocketed to a record $60 million earlier this year. Barack now commands a reported $400,000 for a speaking engagement, while Michelle, also a Harvard-trained lawyer, has taken a much more outspoken role at appearances and in the media.

The couple purchased a nine-bedroom, 8,200-square-foot, Tudor-style mansion in the Washington, DC, neighborhood of Kalorama for $8.1 million earlier this year. A spokeswoman for the Obama family declined to comment.