He's suggested that as many as 1 million people might want to buy one, while Commerce Secretary Howard Lutnick has said 250,000 people were "waiting in line" and "willing to pay the $5 million" fee.

This week, Lutnick told Axios that a website where potential applicants could register their interest would go live within weeks and that further details would follow.

Dominic Volek, thehead of private clients at Henley & Partners, an investment migration consultancy, said the plan was unlikely to generate a rush of applications.

"Their estimations are just simply way off," he told Business Insider. "As a general rule of thumb for wealthy people, they won't spend more than 10% of their liquid net worth on a single discretionary purchase" — whether that's a yacht, a watch, or the right to live in a country.

Volek said that an individual would need at least $50 million in liquid net worth to comfortably part with $5 million.

"Globally, there's probably only 100,000 to 150,000 people who have that kind of net worth, and the majority are already in the US. And so that leaves you with less than 100,000 people as a potential market," he said.

Even if you're quite wealthy, the idea of handing over $5 million rather than investing it may be a tough sell. Many other countries with citizenship or residence-by-investment programs offer tangible returns, not pure capital outflows.

New Zealand offers residency in exchange for a $2.95 million investment, while Singapore requires a $7.8 million investment.

"Those were all investments," Volek said. "That's money I put into the stock market, into a business, into a bond, and I get a return."

The potential tax burden could also discourage applicants. Unlike many countries, the US taxes citizens — and even green card holders living abroad — on their worldwide income.

"It's not a good place to be from a tax perspective," Volek said. "If the tax treatment is not adjusted, then it will be a massive failure."