"It's something we talked about," Trump told reporters on Sunday after they asked about his reported interest in buying the world's largest island, which is politically dependent on Denmark.
Trump acknowledged that "the concept came up" and he believed the "strategically interesting"-part, but added that the issue was not a priority.
"We're very good allies with Denmark. We protect Denmark as we protect large portions of the world," he said.
Earlier in the day, White House Economic Adviser Larry Kudlow had said that Trump was "looking" at possible purchase of Greenland. "I don't want to predict an outcome. I just know the president, who knows a thing or two about buying real estate, wants to take a look at a potential Greenland purchase," Kudlow said.
The US media had first revealed on August 15 that Trump had asked his advisers at the White House to find out if it was possible to buy Greenland from Denmark.
Many years ago, President Harry Truman (1944-53) also wanted to buy that island, Kudlow said. Truman offered Denmark $100 million then for the huge, ice-covered island after the end of World War II.
Trump's interest in the island was not clear. Some speculated that it was because of the island's natural resources while others thought it was due to its geostrategic importance because of its proximity to the Arctic.
Greenland is an island located to the northeast of Canada. About 75 per cent of its surface is covered by ice and is inhabited by only about 56,000 people, mostly of Inuit ethnicity.
Although Greenland politically belongs to Denmark, it is an autonomous territory that since 2009 has governed itself in all aspects but foreign, defense and monetary policy.
( With inputs from IANS )