This is groundless speculation based on recurring lost sovereignty narrative frequently promoted by pro-Kremlin disinformation sources, this time built around the claim that Denmark is a US's vassal country, which will have to please Trump and give up Greenland.
The 2014 Wales Summit Declaration formalised the aim to move towards 2% of GDP spending on defence for all NATO members. Although Denmark is among those NATO countries whose spending has not reached this benchmark, it is not true that Denmark did not pay for defence at all as alleged (see NATO countries defence expenditures for the last years here).
Generally, the issue of US-Denmark negotiations over fair defence spending is well known, however it has nothing to do with Denmark's governance arrangements with Greenland. Danish Prime Minister Mette Frederiksen called Trump's statements on Greenland “an absurd discussion.” Both she and Greenland leader Kim Kielsen responded that Greenland is not for sale. “A discussion about a potential sale of Greenland has been put forward. It has been rejected by Greenland Premier Kim Kielsen and I fully stand behind that rejection,” Frederiksen stated.
Despite the unusual spat over Greenland, the US and Denmark remain allies. Denmark remains sovereign in its domestic and foreign policy as decided by the Danes themselves, including on the matter of the country's relations with semi-autonomous Greenland.
See earlier disinformation cases claiming that Washington is behind Denmark's attempts to obstruct the construction of Nord Stream 2, that Poland is the ''Trojan horse'' of the US, and that the EU has become the vassal of the US.