When Danny Brandt picked up an older man in his cab on Wednesday outside a hotel in downtown Nuuk, the capital of Greenland, he thought the passenger was just another visitor.

Dressed in casual clothes and carrying a stack of papers, the man seemed friendly enough and identified himself in an American accent as Cliff from Las Vegas.

Then he made an intriguing proposal.

“Do you want to earn $200,000?” he asked, according to Mr. Brandt. All he, or any Greenlander, had to do was sign a petition he held in his hand to join the United States.

“No, thanks,” Mr. Brandt responded before dropping him off at another hotel a few minutes later. Then he called the police, who told The New York Times that officers have begun investigating.

The offer might seem ridiculous and futile. Most Greenlanders have indicated they have zero interest in becoming Americans. But the proposal has created a stir in Nuuk because of President Trump’s repeated threats to annex the isle and the recent accusations of covert American activity in Greenland, which is a semiautonomous territory of Denmark.

Police officials in Greenland remain tight-lipped but said the case could be connected to the “current political situation.”