A US news site has reported that the Danish government sent private messages to US President-elect Donald Trump's team showing willingness to discuss issues related to Greenland, such as boosting security on the island.

Trump has said that the United States should claim Greenland, an autonomous Danish territory, for national security purposes. He suggested that China and Russia are increasing their activities near the island.

The report made by Axios on Saturday citing sources with knowledge of the issue says that messages were sent in recent days in which the Danish government made clear that Greenland is not for sale.

The report says however the government expressed readiness to discuss any other US requests, and mentioned a possible expansion of the US military presence on the island.

Observers see the reported action by the Danish government as an effort to find out what Trump exactly wants in order to avoid a public clash with the new US administration.

The US military has a base on Greenland tasked with missile early warnings. Most of the island is in the Arctic Circle, and the existence of rare earth elements is attracting attention in recent years.

Denmark's Prime Minister Mette Frederiksen said she plans to have talks with Trump after his inauguration on January 20.