Slim bought the Fifth Avenue mansion, which faces Central Park at East 82nd Street, for $44 million back in 2010.
If he gets his $80 million, that would make it the most expensive mansion ever sold in the city, the New York Daily News reports.
The eight-story, 20,000-square-foot Beaux-Arts building is one of those landmark mansions that has its own name - or, in this case, names.
Known as the Benjamin N. and Sarah Duke House, the Duke-Semans Mansion, or the Benjamin N. and Sarah Duke House, it's one of the last private mansions on Fifth Avenue, according to the Sotheby's listing.
Built from 1899-1901, the mansion has a French Renaissance interior and was originally owned by an American Tobacco Company tycoon, according to the New York City Landmarks Preservation Commission.
It features high ceilings, hand-carved wood paneling, and gold-leaf trimmed fixtures, and plaster friezes, as well as a "sweeping" staircase, according to the listing.