Ildefonoso Guajardo told his country's Televisa network that he doesn't see a deal happening by Thursday, which the U.S. Congress calls the latest possible date to get a deal in order to have time to vote on it this year.
Under the USA "fast track" trade negotiation law, there are lengthy notification periods before Congress could start considering a new NAFTA, precipitating the establishment of this Thursday's deadline.
"We will keep negotiating, and in the moment that we have a good negotiation, we can close the deal. independent of which Congress [the current or new one] that will vote on it", he said.
Mexico's top trade negotiator said Tuesday that he doesn't believe an agreement between his country, the US and Canada will be reached by Thursday's informal deadline.
Canadian Prime Minister Justin Trudeau and U.S. President Donald Trump spoke on Monday and discussed the possibility of bringing the NAFTA talks to a "prompt conclusion", Trudeau's office said.
"They have failed to reach an agreement, and the divisions are fairly fundamental, so I'm not certain that even if Ryan comes back and says, 'I didn't really mean it, there's wiggle room, ' that it's going to make a difference", Alden said.
"It could be before the Mexican election on July 1, it could be just after", he said.
Chief Mexican NAFTA negotiator Kenneth Smith said that the administration of President Enrique Pena Nieto had a responsibility to keep negotiating until Mexico's new president, who will be elected on July 1, takes office on December 1.
He says Trudeau told the USA president that the ingredients are there for a deal, but Guajardo also says the American side needs to drop some of its impractical proposals.
In the five-month period between election day and the swearing-in ceremony, Guajardo said, the next government's team would need to be involved in any ongoing trilateral trade talks.
However, talks still faced the hurdles of USA demands for a sunset clause that would allow NAFTA to expire if it is not renegotiated every five years, and the elimination of settlement panels for trade disputes. Neither Canada nor Mexico wants that.
More flexibility was needed for a deal, Guajardo said.
Kenneth Smith, the chief Mexican negotiator at the talks, said that for Mexico there were no deadlines in the revamp.
Officials from Canada and Mexico were in D.C. last week working on the terms of a deal, but nothing was reached.