CBS News confirmed Mr. Trump asked his aides and the White House counsel to look into the possibility of buying the island, which is an autonomous Danish territory. It's home to Thule Air Base, the U.S. military's northernmost base.
According to the Wall Street Journal, Mr. Trump proposed the idea multiple times with "varying degrees of seriousness." But Danish politicians have been quick to dismiss it.
"It must be an April Fool's Day joke ... but totally out of season!" former Prime Minister Lars Løkke Rasmussen tweeted.
"No thanks to Trump buying Greenland!" member of Parliament Aaja Chemnitz Larsen said.