President Donald Trump confirmed on Sunday that he's "interested" in buying Greenland. The only problem? It's not actually for sale.

"It's something we talked about," he told reporters on Sunday. "Denmark essentially owns it, we're very good allies with Denmark." Referring to the theoretical transaction as "essentially" a "large real estate deal," Trump said that "strategically it's interesting and we'd be interested, but we'll talk to them a little bit." While he acknowledged that "first we have to find out whether or not they have any interest," he said that, "they're losing a tremendous amount of money, so we'll see what happens."

But officials in Greenland have repeatedly said that it's not for sale. And Denmark confirmed on Sunday that it's not interested in selling the island.

“Greenland is not for sale," Danish Prime Minister Mette Frederiksen told the newspaper Sermitsiag on Sunday. "Greenland is not Danish. Greenland belongs to Greenland. I strongly hope that this is not meant seriously."

Trump's interest in acquiring the 811,000-square-mile island in the North Atlantic was first reported last week by The Wall Street Journal. Citing sources familiar with the deliberations, the Journal reported that Trump has mentioned the idea with "varying degrees of seriousness." NBC News confirmed the president's interest in such an acquisition.

Earlier on Sunday, top White House economic adviser Larry Kudlow told "Fox News Sunday" that the U.S. was "looking at" purchasing Greenland.

"It's an interesting story," Kudlow told host Dana Perino. "It's developing. We're looking at it. We don't know."

Kudlow noted that "years ago," then-President Harry Truman sought to purchase the massive island off the Canadian coast.

"Denmark owns Greenland. Denmark is an ally," Kudlow added. "Greenland is a strategic place up there and they've got a lot of valuable minerals. I don't want to predict an outcome. I just know the president, who knows a thing or two about buying real estate, wants to take a look at a potential Greenland purchase."

Trump is scheduled to visit Denmark next month in an unrelated appearance.

The island of roughly 56,000 people is rich in mineral resources and houses an American airbase. At least twice previously, in 1867 and 1946, the U.S. has tried to buy Greenland. Truman offered $100 million but Denmark turned down the offer.

Officials in Greenland strongly indicated there was no opportunity for such a deal to be made. Greenland's Ministry of Foreign Affairs tweeted that the island is "open for business, not for sale."

Kim Kielsen, Greenland's premier, also said in a statement that the island "is not for sale and cannot be sold, but Greenland is open for trade and cooperation with other countries — including the United States.”

Speaking to NBC News, Anna Kûitse Kúko, 63 and a lifelong resident of Greenland, said she believes islanders take the idea "as a sick joke by a crazy president."