"I spoke to the US president regarding the security situation in Greenland and the Arctic. We will continue to work on this and I look forward to meeting him in Davos later this week," the post reads.
Trump will attend the World Economic Forum being held in the Swiss Alpine idyll next week.
Trump threatened on Saturday to impose tariffs on Sweden, Denmark and several other countries if the US is not allowed to take over the world's largest island.
The EU has consistently opposed an American takeover and underlined Greenland's sovereignty, while Danish Prime Minister Mette Frederiksen has warned that such a move by Washington would spell the end of NATO.
