"We are open for business but we're not for sale", Ane Lone Bagger told the news outlet.
Mr Trump's plans have also been quickly dismissed by politicians in Denmark. "It has to be an April Fool's joke".
The 73-year-old has reportedly even sought out the opinion of the White House counsel on this purchase - however, the Wall Street Journal wrote that his inquiries came "with varying degrees of seriousness".
Sources quoted in other media differed over whether the president was joking or seriously hoping to expand United States territory.
It wouldn't be the first time an American leader tried to buy the world's largest island, an autonomous territory of Denmark.
Greenland is situated between the Atlantic and Arctic oceans.
It has a population of about 56,000 people concentrated around the coastline.
Greenland is located roughly 3,025 miles from the United States. Though 80% of the island is covered in ice, it is rich in natural resources including oil, uranium, diamonds, gold and rare earth elements.
How would Trump go about buying Greenland? .
Why would it be appealing to Trump?.
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Asked if she did not find it flattering that Trump found Greenland attractive, she said: "It is Greenland's geostrategic location that Trump is interested in". It is home to almost 57,000 people, most of whom belong to the indigenous Inuit community. It has high rates of suicide, alcoholism and unemployment. There's also its important strategic role (which we'll touch on later).
Republican Representative Mike Gallagher described Mr Trump's reported idea as a "smart geopolitical move". Greenland is not for sale As of now Greenland can not be sold by Denmark. There are far more pressing problems to be dealt with, though honestly if Trump wants to twiddle his thumbs and focus on buying Greenland rather than continuing to enact deeply harmful practices like supporting ICE detention centers or nominating more Kavanaughs to the Supreme Court, maybe he should do this.
"My immediate thought is 'No, thank you".
Martin Lidegaard, senior lawmaker of the Danish Social Liberal Party and a former foreign affairs minister, called the idea "a grotesque proposal" with no basis in reality. Denmark itself can't sell Greenland because of the home-rule law of 2009 that states that Greenlanders are their own people. The remark was one of several from local residents who reacted with a mixture of mockery and anger to the reports, which originated with an article in The Wall Street Journal on Thursday.
"I strongly hope that this is not meant seriously", Danish Prime Minister Mette Frederiksen told the newspaper Sermitsiaq during a visit to Greenland.
Trump is scheduled to visit Denmark in two weeks. In 1867, the USA reached a deal with Russian Federation to purchase Alaska for $7.2m.
The Wall Street Journal (WSJ) on Thursday cited unnamed advisors as saying the U.S. leader asked his staff to "look into the idea" of purchasing the world's largest island.
However, Duke University law professor Joseph Blocher told the BBC that the practice "has basically dried up".
"Countries should be wary of piling on monumental debt, particularly "loan to own" projects, that undermines their freedom of political action and sovereign choices", a Pentagon official, Johnny Michael, said previously. Needless to say, Greenland has clearly stated it's not on the market. The US bought the US Virgin islands from Denmark in 1917.
There is no indication that the purchase will be on the agenda for his talks with Danish officials.
In 1946, then-President Harry Truman put in an unsuccessful $100 million offer for the territory.