A Wall Street Journal report outlining the U.S. president’s apparent interest in a deal left Danes bewildered, with a former prime minister asking if it was a joke. A member of the ruling political bloc in Denmark, which helps run Greenland as an autonomous territory, called it a “terrible idea.”

The Journal, citing people familiar with the deliberations, said Trump has repeatedly expressed interest in a purchase and even asked his White House counsel to explore the idea. While the island’s 83,000 square miles (2.2 million square kilometers) are mostly icy wilderness, Greenland is also home to Thule Air Base, the U.S. armed forces’ northernmost installation.

Trump’s suggestion “must be an April Fool’s Day joke” out of season, tweeted Lars Lokke Rasmussen, who was prime minister until June and now heads the opposition in Denmark. In the U.S., there were mixed reactions. Republican Representative Mike Gallagher said the U.S. “has a compelling strategic interest in Greenland, and this should absolutely be on the table.” Representative Steve Cohen, a Democrat, said the idea might work as a “cryonic memorial.”

The Journal report comes as Trump prepares for his first formal visit to Denmark on Sept. 2-3, when he’ll meet with Prime Minister Mette Frederiksen and attend a state dinner hosted by Queen Margrethe II. Greenland will be one focus of the meetings. The U.S. presence there hasn’t always been in the news for the right reasons: In 1968, a B-52 bomber carrying nuclear weapons crashed near the Thule base in northwestern Greenland, causing radioactive contamination.

In a statement headlined “Greenland Isn’t for Sale,” Christian Juhl, a member of the Red-Green Alliance that’s part of Denmark’s government bloc, had a counter-proposal: “Trump can instead offer to pay rent for the Thule base, which until now has been made available to the U.S. for free.”

Frederiksen, who became prime minister after her Social Democratic party won the June election, will make a first official visit to Greenland next week for talks with the island’s premier, Kim Kielsen. While Greenland is self-administered, defense and foreign affairs remain under Danish governance. The island has its own representation in Washington and Brussels.

More than 80% of Greenland is covered in ice. It’s become a focal point of climate studies because the island’s glaciers are melting at a record pace. Greenland’s population of just 56,000 is concentrated on the coasts.

The Wall Street Journal, noting that it’s unclear how Trump would go about acquiring the Danish territory, said neither the White House nor the State Department responded to a request for comment.

Worth Knowing About Greenland:

Greenland, in the north Atlantic ocean between Europe and America, has been a nexus of geopolitical tensions between the U.S., Russia, Canada, Denmark and Norway. All those nations have sought ownership of the natural resources near the North Pole.

In 2014, Denmark staked a claim to roughly 900,000 square kilometers of the continental shelf in the Arctic Ocean based on its geological link to Greenland, according to a survey conducted by Danish authorities.

More recently, China joined the scramble for territory by bidding for two airport construction jobs in Greenland. Last year, Denmark opted for joint funding with Greenland to prevent China getting control.

Greenland, which gets most of its income from fishing and related industries, had a gross domestic product of just over $2.7 billion in 2017, according to its statistics office. The island receives an annual subsidy of about $500 million from Denmark.