Since returning to the White House in January, Trump has repeatedly said the United States needs the strategically located, resource-rich island for security reasons, and has refused to rule out the use of force to secure it.
At least three US officials close to Trump have been noticed in Greenland's capital Nuuk trying to identify people they could use in anti-Denmark influence campaigns, according to Danish public television network DR.
Foreign Minister Lars Lokke Rasmussen said in a statement to AFP he was aware of "foreign actors" showing an interest in Greenland's posoition within Denmark.
"Any attempt to interfere in the internal affairs of the Kingdom will of course be unacceptable," he said, adding that he had "asked the ministry of foreign affairs to summon the US charge d'affaires for a meeting at the ministry".
Most of Greenland's 57,000 people want to become independent from Denmark, according to a January poll, but do not wish to become part of the US.
Both Denmark and Greenland have repeatedly insisted the Arctic island is not for sale and that it will decide its future itself.
Prime Minister Mette Frederiksen said she was taking the matter seriously.
"I note that the Americans have not clearly rejected the DR report today, and that is of course serious," she told Danish television.
The Wall Street Journal reported in May that US intelligence agencies had been ordered to find out more about Greenland's independence movement and opinions on American exploitation of resources.
According to the newspaper, intelligence agencies had been asked to identify people in Greenland and Denmark who supported US objectives.
Frederiksen reacted angrily to that report at the time, saying: "You cannot spy against an ally."
Like the United States, Denmark is a founding member of NATO and has recently fought alongside America in its wars in Afghanistan and Iraq.
- Sowing discord -
According to the DR report on Wednesday, the US officials were trying to gather information on issues that have created tension between Greenland and Denmark -- which could be used to present Denmark in a bad light.
These include Denmark's forced removal of Greenlandic Inuit children from their families, as well as its forced contraception of at least half of all fertile Inuit women from the 1960s until 1992.
Frederiksen on Wednesday presented a long-awaited apology to the 4,500 Inuit women who had to wear a contraceptive coil -- or intrauterine device (IUD) -- without their or their family's consent.
"We cannot change what has happened. But we can take responsibility. Therefore, on behalf of Denmark, I would like to say: I am sorry," she said in a statement.
- US provocation -
In March, US Vice President JD Vance made an uninvited visit to Greenland that was widely seen as a provocation both on the island and in Copenhagen.
He was initially due to tour several towns but following angry reactions across Europe, he shortened his itinerary to a one-day visit of the US Pituffik military base.
During a speech there, Vance castigated Denmark for not having "done a good job by the people of Greenland", alleging it had neglected security.
The Pituffik base is an essential part of Washington's missile-defence infrastructure, its location putting it on the shortest route for missiles fired from Russia at the United States.
The Arctic has gained geostrategic importance as the race for rare earths heats up and as melting ice caused by global warming opens up new shipping routes.
Copenhagen in January announced a $2-billion plan to boost its military presence in the Arctic region.
Ahead of Greenland's March 11 general election, Denmark's intelligence service said it was concerned about possible foreign interference, particularly from Russia, but said no attempts were ever detected.
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