Twitter users have had a field day at the news.
Actress Bette Midler wrote: 'Trump wants to buy Greenland? Let’s make him find it on a map first.'
A former national press secretary to Hillary Clinton jokingly compared it to Trump's bold campaign promise that Mexico would pay for a border wall.
'Donald Trump is going to buy Greenland and Mexico is going to pay for it,' wrote Jesse Ferguson.
Meanwhile writer Jon Gabriel posted an image of a town in Greenland with a huge golden Trump Tower photoshopped in, with the caption: 'Greenland in 10 years.'
One confused Twitter user questioned: 'We...might be buying Greenland?' while another posted a meme with the caption: 'Me seeing Greenland trending. "I wonder what this is abou..."'
One Twitter user wrote alongside a meme of Homer Simpson slowly retreating into a bush: 'BREAKING NEWS: Denmark to relocate Greenland in undisclosed location due to safety concerns.'
Alongside a meme of two laughing men, one person said: 'Danes waking up this morning and finding out that @realDonaldTrump wants to buy #Greenland.'
One person with the Twitter username 'Antfarmer' made use of the 'Distracted Boyfriend' meme. 'Someone had to... #Greenland #GreenlandNewDeal,' they wrote.
'Trump suggests we buy Greenland. Denmark be like,' another person posted.
The 811,000-square-mile island of icy terrain in the Atlantic inhabits about 56,000 people, and though it is technically in North American waters, the self-governing land is culturally European.
Its foreign and security policy is handled by Copenhagen.
According to the Journal, Greenland relies on $591 million of subsidies from Denmark annually, which make up about 60% of its annual budget.