The Metropolitan Museum of Art is playing head games with an antique dealer who claims its 12th-century sculpture of King David’s noggin is a fraud.

Robert Walsh, 62, took an interest in the Met’s sculpture after he bought a very similar head at a Greenwich Village antique store for $600 in 2012.

But when he first visited the Met’s King David, he knew instantly that the fine-grained, grey limestone head — which the museum contends once graced a portal at Notre Dame Cathedral in Paris — is not the real thing.

He believes it is a knock-off made between 1919 and 1920 in Paris, and that the model may have been his own, valid sculpture.

The Met sculpture was acquired by “Monuments Man” James Rorimer, a curator of medieval art for the museum who was played in the 2014 movie “Monuments Men” by Matt Damon.

Walsh, who says his head is worth up to $20 million, expected the Met to embrace his findings. Instead, he has been consistently rebuffed since he came forward in 2012.

Walsh has spent the last five years immersed in research. He has had his head scientifically tested and even traveled to Paris to consult with experts. In 2014, a piece of the limestone from Walsh’s sculpture was drilled and tested by experts from the University of Missouri, which has a database of samples of antique French limestone. Walsh’s sculpture was found to contain traces of limestone from a quarry in the Burgundy region of France, proving that the head is indeed of French origin and an antique.

His research has also revealed that the Met’s head was originally for sale from a dubious French gallery that trafficked in fakes.

French art dealer Georges Demotte employed one of France’s greatest forgers, who turned out “antiquities” that were sold to the Louvre and the Metropolitan Museum in the 1920s and 1930s. Walsh believes that Demotte’s Paris-based forger used his head to make the Met’s sculpture.

In a landmark French investigation in 1923, Demotte’s New York agent Jean Vigoroux, called Demotte “the world’s greatest faker,” according to newspaper reports of the day. Vigoroux told a French court that Demotte “has inundated America with false art,” and said that the gallery had sold at least six fakes to the Met.

The Met’s head was first offered for exhibit and sale at Demotte’s New York gallery in November 1930. The catalog lists the object as “Crowned King’s head.” There is no mention of King David or Notre Dame. In fact, the catalog’s preface says that the head was found “in Paris in the environs of St. Germain de Pres,” which is across the River Seine from Notre Dame.

The Met’s head was purchased for the museum by Rorimer in 1937 for $2,500 to display at the The Cloisters, the Met’s medieval art museum in northern Manhattan. Rorimer bought it from the art dealer Arnold Seligmann, who acquired the head after Demotte’s son’s death in 1934.

In that same year, the Louvre in Paris bought a similar head from Demotte’s New York gallery. After Walsh contacted the famed French museum two years ago, the head was removed from public display.

“I suddenly discovered there was something very wrong,” said Walsh. “The museum’s story of their head is a lie.”

And he is worried that the Met’s refusal to acknowledge the true history of its sculpture will prevent him from cashing in on his.

The Met maintains that its head is the real thing. A spokesman said, “The Met’s Head of King David is an important example of early gothic French sculpture that the Met is proud to feature in its medieval galleries. Our firm conclusion after extensive research is that the piece is indeed authentic, and connected to comparable works produced in Paris in the twelfth century.”