US President Donald Trump has said migrants at the US-Mexico border will stay in Mexico until their asylum claims are individually approved in US courts, but Mexico's incoming government has denied striking any deal.

Key points: Mr Trump says the US will close the border with Mexico if necessary

Mr Trump says the US will close the border with Mexico if necessary But Mexico's incoming interior minister Olga Sanchez Cordero says no deal has been made with the US

But Mexico's incoming interior minister Olga Sanchez Cordero says no deal has been made with the US Ms Sanchez Cordero rules out Mexico becoming a "safe third country" for migrants

Their comments came on the back of a report in The Washington Post, which claimed Mexico and the US had agreed on a deal named Remain in Mexico.

The plan, according to the newspaper, foresees thousands of migrants staying in Mexico while their asylum claims in the United States are being processed.

This could potentially end a system Mr Trump has decried as "catch and release" that has, until now, often allowed those seeking refuge to wait on safer US soil.

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But Mexico's incoming interior minister Olga Sanchez Cordero said there was "no agreement of any type between the future government of Mexico and the United States".

Ms Sanchez Cordero ruled out that Mexico would be declared a "safe third country" for asylum claimants.

Thousands of migrants are in Tijuana, right on the Mexico-US border. ( AP: Gregory Bull )

If Mexico were to assume "safe third country" status, asylum seekers would be required to claim refugee status in Mexico rather than the United States, and activists have long argued Mexico does not have the security conditions to offer safe haven for Central American migrants fleeing poverty and violence.

Ms Sanchez Cordero, the top domestic policy official for president-elect Andres Manuel Lopez Obrador — who takes office on December 1 — said the incoming government was in talks with the United States.

But she said they could not make any agreement on the issue, since they are not yet in government.

Mr Trump is seeking to block thousands of Central Americans travelling in caravans from entering the United States, and has ordered that immigrants who enter the country illegally from Mexico are ineligible for asylum.

That order has been temporary suspended by a US judge.

During his Thanksgiving break, Mr Trump also threatened to close entry into the country from the southern border.

Sorry, this video has expired Donald Trump has been vocal on a range of topics during his Thanksgiving break

Managing attorney for the Los Angeles office of legal rights organisation Human Rights First, Jenna Gilbert, said Mr Trump's new plan is "outright illegal, and I'm sure the administration will once more see itself in court".

The Washington Post article cited Mexican officials and senior members of Mr Lopez Obrador's transition team.

It said the deal would break with long-standing asylum rules and mount a new obstacle for Central American migrants attempting to seek refuge in the United States.

Mexico's incoming deputy interior minister, Zoe Robledo, said details of the Remain in Mexico scheme were still being worked out.

"What we're aiming for is that people leaving their countries due to security issues or violence can find a place to stay in Mexico, if that is their decision," Ms Robledo said.

Sorry, this video has expired Thousands of trekking migrants hope to reach the US as their new home.

Ms Robledo said the incoming government wanted to find jobs for Central American migrants in sectors that are short-staffed, such as maquila assembly plants.

Mr Lopez Obrador has vowed to try to eliminate the causes of migration by creating more jobs and improving living conditions in Mexico and Central America.

In exchange, he hopes Mr Trump and the Canadian government will agree to help spur economic development in the region.

Outgoing President Enrique Pena Nieto has also sought to stem the flow of migrants north by offering jobs to them, and has received backing from the private sector in his efforts.

Reuters