The US President tweeted a photoshopped picture of his landmark building looming over a small village in the Arctic territory.
He tweeted: “I promise not to do this to Greenland!”
President Trump admitted on Sunday that he was "strategically" interested in buying Greenland from Denmark, but added it was not his administration's top priority.
"It’s not number one on the burner,” president Trump said.
Denmark's prime minister Mette Frederiksen has told Mr Trump that Greenland is not for sale, and dismissed any suggestion that the US could buy the territory.
Greenland responded to reports Mr Trump had spoken to aides about purchasing the territory from Denmark.
In a statement on the island government’s website, a spokesman said: “We have a good cooperation with USA, and we see it as an expression of greater interest in investing in our country and the possibilities we offer.
“Of course, Greenland is not for sale.”
The story was originally reported by the Wall Street Journal, and it was met with mixed reactions on whether it was a joke or a serious proposal.
Greenland's Ministry of Foreign Affairs also made their point on Twitter, stating: "Greenland is rich in valuable resources such as minerals, the purest water and ice, fish stocks, seafood, renewable energy and is a new frontier for adventure tourism.
"We're open for business, not for sale."
Former Prime Minister Lars Løkke Rasmussen sent out a tongue-in-cheek tweet in response, stating: "It must be an April Fool’s Day joke ... but totally out of season!"
The territory's former foreign minister also spoke out against the news, tweeting: "Trump buying Greenland ?!
"Hopefully a joke, but otherwise terrible thought with the risk of militarization of Greenland and less independence for the Greenlandic people - besides great loss to Denmark."
It wouldn't be the first time a country has tried to buy its way into owning part or all of Greenland.
In 1946, then-US president Harry Truman proposed to pay Denmark $100 million (£82.3 million) to buy Greenland, after flirting with the idea of swapping parts of Alaska for that in the Arctic.
China also recently bid for airport construction jobs on the territory, before Denmark intervened.