The Washington Post reported that a potential deal to avoid the tariffs would allow the United States to deport asylum seekers from Honduras and El Salvador to Guatemala, which they pass through to get to Mexico and then the United States.
Ebrard's spokesman Robert Velasco Alvarez said Thursday that there was no deal as the two sides were far apart, but that talks continue.
"The US position is focused on migrant control measures, ours is on development," he said, referring to Mexico's support of a broader effort to support the economies of Honduras, El Salvador and Guatemala.
At Mexico's southern border Thursday, there were visible efforts to slow the migrants and hinder their supporters.
In the southern state of Chiapas, AFP journalists reported an increased police and military presence on roads typically used by migrants heading north. Ebrard confirmed that 6,000 National Guardsmen would be deployed to the border.
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Mexico City froze the bank accounts of 26 suspected human traffickers allegedly responsible for organizing US-bound migrant caravans.
Two activists from People Without Borders (Pueblo Sin Fronteras), which has helped organize migrant caravans, were arrested on allegations of offering migrants money to enter Mexico illegally.
Mexican authorities also blocked 420 migrants in a new caravan, although the group was initially about 1,200-strong, with many suspected of running away before immigration officials stepped in.
- Asylum not the problem -
Meanwhile Carla Provost, the head of the US Border Patrol, downplayed the issue of asylum, saying migrants simply understand that, due to US laws, if they arrive with children, they will likely be released into the United States.
She noted that since October, 230,000 children without legal travel documents have crossed the border into the United States, most with families but also tens of thousands unaccompanied by adults.
"The issue is they don't even have to claim asylum, they know that," Border Patrol chief Carla Provost told CNN.
"They are telling us they are told by smugglers, they are hearing announcements in their own country, that if they come right now and bring a child, they will be released," she said.
"That is a true statement, because we cannot hold them longer than 20 days if they have a child."
