The Department of Homeland Security said this past week that the wall would cost $21.6 billion and take three and a half years to construct.
With 654 miles (1,046 km) of the border already fortified, the new construction would extend nearly the length of the entire border.
Shortly after his inauguration Trump ordered work to begin on building the wall along the 2,000-mile (3,200-kilometer) US-Mexico border - one of his signature campaign promises - in a bid to block migrants from illegally entering the United States.
At a House Homeland Security hearing earlier this week, Secretary Kelly did not address the funding of the wall, though he did give the panel an estimate on its timing.
DHS said in a statement, "As a matter of policy, we do not comment on or confirm the potential existence of pre-decisional, deliberative documents".
The report assumes funding would be granted by April or May, and that construction could commence in September. In the past, Trump has repeatedly said Mexico will pay for the wall at a later date, with Congress (so, American tax dollars) fronting the funds at first. Under this plan, the US would refrain from taxing American companies' exports, but would tax imports.
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Already the USA government has begun seeking waivers to address environmental laws on building in some areas, the report indicates.
In remarks to law enforcement officials in Washington on Wednesday, Trump reported that the wall was being designed "right now".
The report also indicates that the project will require Trump to enforce "eminent domain", a principle which allows the federal government to seize private land "in the national interest", and which is highly controversial among many of Trump's core supporters who rail against "big government". The final phase will cover the remaining areas. If all goes according to plan, the wall could be completed just in time for the 2020 presidential election.
Reuters quoted a source within DHS saying that the Trump administration would likely need to seize hundreds of miles of the privately-owned borderland from us citizens under eminent domain in order to embark on the final phase.
Bernstein Research, an investment research group that tracks material costs, said that uncertainties around the project could drive its cost up to as much as $25 billion (£20 billion).