But a House Appropriations Committee aide told CQ Roll Call on Thursday night that the committee had not heard from the Trump transition team about building a wall with taxpayer money rather than billing Mexico, as Trump promised during his campaign.
Trump said during the campaign that the cost for building a border wall would be about $12 billion.
Congress would be asked to ensure that enough money is appropriated to take additional new steps - but would not pass a stand-alone bill authorizing a big new wall. Republicans, and Trump himself, are now talking about a combination of fencing and wall.
Trump's statement that the US will be "paid back by Mexico later" is a smoke-and-mirrors attempt to instill hope in his most gullible supporters. Trump said at a rally in Gettysburg, Pa. on October 22.
The US Congress is exploring ways to pay for a southern border wall, with payment to be sought from Mexico later.
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Despite the confusion over who will pay for the wall, many people are still horrified by the prospect of this structure being built at all.
But getting Mexico to pay the invoice for Trump's "Great Wall" is probably going to prove to be hard. "Congress is taking it on themselves to explore different options to pay for the wall", Conway said in an interview with CBS News.
It came as House Republicans revealed Mr Trump's plans to use public funds for the estimated $14 billion (£11 billion) project, in a U-turn on his repeated pledge to make Mexico fund the wall outright.
Trump has said his wall would cost between $8 billion and $12 billion to build, according to Politifact, which adds that some independent estimates have predicted the cost of construction could end up costing up to $25 billion. Funding the wall through a large appropriations bill could force Democrats to choose between continuing to pay for government operations, or stopping the wall. Any effort on Trump's part to use these reimbursements to cover the alleged cost of a border wall, then, would likely result in a myriad of lawsuits that the Federal Government would in all likelihood lose.
In fact, the 2,000 mile border block was number one on Trump's 10-point immigration plan, in which he vowed the colossal structure would be paid for by Mexico's government.