Greenland's prime minister has said the island is "not for sale" after reports Donald Trump has discussed trying to buy the northern territory from Denmark as a way to expand America.

"Greenland is not for sale and cannot be sold," said Kim Kielsen, "but Greenland is open for trade and cooperation with other countries, including the USA."

The US president's proposal, which was first reported in the Wall Street Journal, has come with “varying degrees of seriousness”, though he has apparently gone as far as seeking the view of the White House counsel.

Mr Trump discussed the idea at a dinner last year at which he said he had heard Denmark found the financial support to the territory burdensome, the Journal reported.

Reuters reported two sources familiar with the situation as saying he had privately discussed the idea with aides and advisers, with the notion laughed off by some as a joke but taken more seriously by others.

Danish politicians hit back strongly on Friday at the suggestion that the US could purchase buy the glacier-covered island. One party spokesman for the autonomous territory told the US to "forget it".