The White House made the request after Trump revealed his first budget proposal on Thursday.
Critics of the budget plan were quick to reject its underlying premise that the border is out of control and billions more need to be spent on security issues.
The president says it will cost about $12 billion but U.S. Secretary of Homeland Security John Kelly estimated the cost at $21 billion.
But Hidalgo County officials are not the only ones interested in helping to build the border wall.
Customs and Border Protection posted its notice for the request for proposal (RFP) on Friday evening.
Trump's proposal also suggests the president is gearing up for legal challenges to his immigration enforcement machinery. The request from the Customs and Border Protection Department called for a 30-ft-high wall, but said that plans to build a wall minimum 18 ft in height may be acceptable. The proposed designs should ideally create a 30-foot wall, though the department will consider barriers as small as 18 feet, Reuters reports.
The wall must also include "anti-climb topping features" in order to prevent people from scaling it with grappling hooks or handholds, and it should be built at least six feet "below the lowest adjacent grade" so would-be border-crossers can't simply burrow under it. The request specifically mentions it must successfully endure for at least 30 minutes - but ideally more than four hours - attempts to bore through it with a "sledgehammer, vehicle jack, pick axe, chisel, battery operated impact tools, battery operated cutting tools, Oxy/acetylene torch or other similar hand-held tools".
One request calls for designs of a solid concrete wall, while the other requests plans that incorporate a "see-through component" to the wall for "situational awareness".
With all the other crises assailing us, there has been a hiatus in the debate over the Mexican border wall.
On Tuesday, a company in the central Mexican state of Puebla called Ecovelocity raised eyebrows when it said it wanted to install lighting for the wall.
Both should be "aesthetically pleasing in color" and texture consistent with the general environment, but only from the north side.
The proposals are due to the government by March 29.
The president has vowed to make Mexico reimburse the United States for its cost but Mexico has repeatedly said it will not do so. Judges were previously shifted to two immigration detention centers in California.