It's no longer what the United States was putting first in any way", Jesus Seade, designated chief negotiator of Mexico's next government, told reporters outside the U.S. Trade Representative's office.
On Saturday, he said the US "relationship with Mexico is getting closer by the hour" in a tweet that made no mention of Canada.
Canada's top diplomat and chief NAFTA negotiator Chrystia Freeland said earlier this week that Canada would rejoin the discussions once the bilateral issues between Mexico and the U.S. had been resolved.
Guajardo declined to go into detail on the topics remaining with the United States but said the agreement could happen at any time.
Energy, the Journal reported, was left out of the original NAFTA when it came into force 24 years ago because Mexico's state monopoly on oil didn't allow private investment in the industry. However, on the possibility of a handshake deal, Guajardo said it would have to involve all three countries.
Industry sources say they are close to agreeing on raising the regional automotive content threshold for tariff-free access under NAFTA to around 75 percent from 62.5 percent.
Any handshake agreement announced on bilateral issues between the USA and Mexico would be the biggest breakthrough in negotiations since they began a year ago.
A major trade agreement with Mexico may be coming soon, the US president announced.
But Guajardo told reporters that Canada's Foreign Minister Chrystia Freeland was ready at any point to proceed with the NAFTA negotiations.
On his way into Saturday's talks in Washington, Mexican Economy Minister Ildefonso Guajardo praised the United States president's "optimism", but remained cautious. S. talks have been complicated by divisions between the incoming and outgoing Mexican administrations over energy policy.
He hopes to reduce the US trade deficit with lower-cost Mexico and claw back jobs, particularly in the auto industry. Jesus Seade, the NAFTA representative for Mexican president-elect Andres Manuel Lopez Obrador, on Saturday predicted that the nations will agree on a lighter version of a so-called sunset clause, an automatic expiration after five years - a key USA demand.
Mexicans and US officials have been eager to revise NAFTA by the end of August to give allow the outgoing Mexican administration of Enrique Peña Nieto to sign the deal before leaving office.
Canadian officials have downplayed the significance of their exclusion from recent talks and argued that it is good for the US and Mexico to resolve their own differences on thorny issues like autos and agriculture.
A contentious proposal by the United States - which would require the almost 25-year-old trade pact be reapproved every five years - is one that must include all three partners, Guajardo told reporters on his way in to yet another meeting.
Lopez Obrador, a leftist populist who was elected in a landslide on July 1, said Friday that the NAFTA talks were proceeding well.