President Trump Eyes a New Real-Estate Purchase: Greenland

President Trump made his name on the world’s most famous island. Now he wants to buy the world’s biggest.

The idea of the U.S. purchasing Greenland has captured the former real-estate developer’s imagination, according to people familiar with the discussion, who said Mr. Trump has, with varying degrees of seriousness, repeatedly expressed interest in buying the ice-covered autonomous Danish territory between the North Atlantic and Arctic oceans.

In meetings, at dinners and in passing conversations, Mr. Trump has asked advisers whether the U.S. can acquire Greenland, listened with interest when...