If Greenlanders remain cool to the idea of becoming Americans, perhaps they could be won over with cash payments of $10,000 per person or more, Trump administration officials are reported to be thinking.

The Reuters news agency says four sources “familiar with the matter” have told it the idea has been discussed among U.S. officials, with two of the sources saying the sums being mentioned have ranged as high as $100,000 per person.

The sources did not explain exactly how the process might play out, but Danish officials have acknowledged they would not likely stand in the way if Greenlanders voted to secede from the Danish kingdom, of which the island is a part.

Denmark’s public broadcaster, DR, reported in August that at least three Americans with links to President Trump had been involved in covert operations seeking to encourage Greenland to leave Denmark and join America.

With Greenland’s permanent population totaling just 57,000 people, the reported payouts would cost between $570 million and $5.7 billion. That would be a bargain compared to some estimates of a fair price for the resource-rich island, which range far higher.

“Something in the trillions looks about right,” said the president of a center-right think tank, Douglas Holtz-Eakin, in an interview this week with CNBC. In a study published last year, his group, the American Action Forum, calculated the value of Greenland’s known critical mineral and energy resources alone at more than $4.4 trillion.

Even allowing for the fact that harsh Arctic conditions make most of those resources hard to extract, the study put the minimum value of Greenland’s resources at $186 billion. Adding in the strategic value of the real estate — a factor repeatedly emphasized by Mr. Trump — could boost the island’s fair market value by another $2.8 trillion, the study found.

Other attempts to put a price on Greenland have come up with smaller but still hefty valuations.

In a 2019 exercise begun after Mr. Trump first expressed an interest in acquiring Greenland, the Financial Times’ trader-oriented Alphaville website looked at the island’s known reserves of oil and rare earth minerals as well as its real estate and came up with a “very conservative” valuation of $1.1 trillion.

In a thought experiment last year for the New York Times, a former New York Federal Reserve economist, David Barker, looked at what America paid for Alaska in 1867 and for the U.S. Virgin Islands in 1917, adjusted for inflation and economic growth, and came up with a price tag for Greenland between $12.5 billion and $77 billion.

Since returning to office a year ago, Mr. Trump has repeatedly voiced America’s “need” to possess Greenland for national security reasons, pointing to Russia’s and China’s fast-growing presence in the Arctic.

The president has suggested purchasing the island but Denmark, which has sovereign authority over the territory, has repeatedly insisted that Greenland is “not for sale.” That has led the Trump administration to look to other approaches, leaving open the use of military force.

When Reuters asked the White House for comment on its report about cash payments to all Greenlanders, the agency was referred to remarks this week by the White House press secretary, Karoline Leavitt, and the secretary of state, Marco Rubio.

During a press briefing, Ms. Leavitt acknowledged that Trump and his national security aides were “looking at what a potential purchase would look like.” Mr. Rubio is scheduled to discuss Greenland with Denmark’s foreign minister in Washington next week.

Neither the Danish embassy declined a request for comment from Reuters.