Two advisers told the Journal that Trump asked them and other advisers at dinners and in passing conversations whether such a move would be possible, listening intently when they talked about its resources and geopolitical importance.
He also reportedly asked his White House counsel to look into the idea.
Some of his advisers were supportive of the move, the two sources told the Journal, saying it could be a good economic play. Others dismissed it as just a fascination.
As the Journal noted, it is unclear how the U.S. would go about purchasing Greenland, the largest island in the world.
Roughly 56,000 people live on the mostly self-governing island. Foreign and security policy is handled by Copenhagen.
The White House did not immediately respond to a request for comment about the Journal's report.