President Trump is mulling a tax on cash transfers between immigrants in the U.S. and their relatives in Mexico as a way to fund his promised border wall without forcing American taxpayers to open their wallets, according to sources familiar with the proposal.

Trump first floated the idea of taxing or halting person-to-person wire transfers, known as remittances, during his bid for the White House. A two-page memo released by his campaign last April described a plan "to compel Mexico to pay for the wall" by preventing immigrants from wiring money outside of the U.S. unless they can prove their legal status to law enforcement authorities.

Because the Mexican economy has become so dependent on wages sent home by migrant workers, which surpassed oil revenues as its leading source of foreign income in 2015, Trump said he could convince the country's leaders to make a "one-time payment of $5-10 billion" toward his border wall by threatening to stop the annual flow of billions of dollars from the U.S. to Mexico in the form of cash transfers.

In 2016, Mexican immigrants living in the U.S. sent $27 billion to family members and friends in their native country.

"They will live very, very frugally to save as much money as they can to send it back home," Rep. Mike Rogers, R-Ala., told the Washington Examiner.

Rogers introduced a bill in March to levy a 2 percent tax on all cash transfers from "anybody who remits to South America." The legislation, which is currently stuck in committees, would net a little more than $1 billion a year and "comport with President Trump's pledge to build a wall and make [Mexico] pay for it."

"I went over and met with the deputy chief of staff Rick Dearborn in the White House about two weeks before we left for recess and he told me that they're trying to come up with a package of bills or pay-fors and hopes mine will be part of that," Rogers said in a phone interview Wednesday. "My understanding is that they're trying to find a way to make sure that the money comes from money that would have gone to Mexico otherwise."

One administration official said Dearborn, an immigration hardliner who served as chief of staff to Attorney General Jeff Sessions when he represented Alabama in the Senate, remains one of the driving forces behind Trump's border wall strategy. Dearborn did not respond to a request for comment.

White House spokeswoman Natalie Strom declined to describe any progress the administration has made toward getting Mexico to pay for Trump's wall. Strom told the Washington Examiner she was not at liberty "to discuss these types of questions publicly."

Border wall funding was thrust back into the spotlight earlier this month when Trump told a rowdy crowd in Phoenix that he would rather shut down the government to secure money for his most contentious campaign promise than capitulate on a spending bill that does not include wall money.

"We need the wall, it's imperative," Trump reiterated at a press conference this week. "We may fund it through the United States, but ultimately Mexico will pay for the wall."

Former White House national security aide Sebastian Gorka, who left his post last week, said getting Mexico to pay for a barrier along the southern border "is still a non-negotiable as far as the president is concerned."

"I can tell you, he's not giving up on that," Gorka told the Washington Examiner.

Rogers wants Trump to hold off on aggressively pushing for wall funding until GOP lawmakers score at least one marquee legislative victory. The Alabama congressman said his primary concern is that jumping the gun on a hot-button issue like border security could create a toxic environment on Capitol Hill in which Republican infighting would impede progress on other areas of policy.

"It's my hope that the president will wait until late October before he brings this up, giving us time to work on tax reform and the infrastructure bill," Rogers said, "because when he really makes paying for the wall the dominant theme, it's going to be very politically explosive."

But some pro-border enforcement groups have lost their appetite for a more restrained approach. And they want Trump to rapidly secure the border no matter the cost politically or for taxpayers.

"This, obviously, was a signature promise that the president made in his campaign, so we would like to have seen faster progress on this," said Ira Mehlman, a spokesman with the Federation for American Immigration Reform, a group that has advised the administration on immigration-related issues.

Mehlman said that if Trump no longer believes he can broker a deal that ensures Mexico pays for the wall, "our view is that if we have to pay for it ourselves, it's worth the investment."

"There are creative ways of doing it and taxing remittances is certainly one idea. But we're more interested in the wall being built, protecting the security of the United States, and saving billions each year in the social costs associated with illegal immigration," he said.

The renewed debate over border wall funding comes as the Department of Homeland Security prepares to break ground on a section of the border in San Diego, Calif., where a small group of federal contractors have been invited to construct wall prototypes. A memo circulated by the agency earlier this year put the price tag for a 1,250-mile wall at $21.6 billion, with an estimated completion date sometime in 2020.