“It's something we talked about,” Trump told reporters.
“The concept came up and I said certainly, strategically it's interesting and we'd be interested, but we'll talk to (Denmark) a little bit,” he said, stressing that it was “not number one on the burner” for the government.
The Wall Street Journal reported on Thursday that Trump had expressed interest in the self-governing part of Denmark, asking advisors if it would be possible for the US to acquire the territory.
The president, a former real estate magnate, has been curious about the area's natural resources and geopolitical relevance, the paper said.
When asked if he would consider trading a US territory for Greenland, Trump replied that “a lot of things could be done.”
“Essentially, it's a large real estate deal,” he said.
“It's hurting Denmark very badly because they're losing almost $700 million a year carrying it… and strategically, for the United States, it would be nice,” he added, without offering any evidence for those claims.
Denmark colonized the 772,000 square-mile (two-million square kilometer) island in the 18th century. It is home to about 57,000 people, most of whom belong to the indigenous Inuit community.
Greenland's ministry of foreign affairs insisted Friday the island was ready to talk business, but was not for sale.
“#Greenland is rich in valuable resources such as minerals, the purest water and ice, fish stocks, seafood, renewable energy and is a new frontier for adventure tourism,” it tweeted.
“We're open for business, not for sale,” it added.
Danish prime minister Mette Frederiksen on Sunday dismissed the notion Denmark could consider selling Greenland.
Speaking before Trump confirmed his interest, Frederiksen told Greenlandic newspaper Sermitsiaq.AG she hoped the reports were not serious.
“Greenland is not for sale. Greenland is not Danish, Greenland is Greenlandic. I sincerely hope this is not something that was meant seriously,” Frederiksen told the newspaper.
Denmark’s head of government has also called the idea an “absurd discussion”, in comments to broadcaster DR.
Trump will meet both Frederiksen and Greenland’s PM Kim Kielsen on a state visit to Denmark scheduled for 2nd-3rd September.