Guajardo declined to go into detail on the topics remaining with the United States, but said that an agreement could be reached at any time.
Trump's relationship with Mexico has been strained over his push for it to pay for his border wall.
Trump's trade team has employed a divide-and-conquer strategy in their attempts to renegotiate NAFTA, which they argue was responsible for "stealing" USA manufacturing jobs but which in fact has helped the United States auto sector prosper.
The "sunset clause" - an automatic cancellation of all agreements after five years - has been a major demand from the US administration, but Mexico believes it can agree to a renegotiated version of this. If new terms could not be reached, NAFTA would die. Canada and Mexico are against this because such a pact would create uncertainty, report Reuters. NAFTA has been in effect nearly 25 years.
The office of U.S. Trade Representative Robert Lighthizer, who is leading the U.S. negotiating team, did not respond to an emailed request for comment. "He's a man whose style I really like", Seade said.
But experts remain skeptical, especially given Canada's absence in the latest round of negotiations, and some are questioning the legality of the bilateral deal.
Guajardo, the top Mexican negotiator, told reporters in Washington that it would take at least a week to finalize the deal once Canada re-enters the talks.
"Nothing is done until everything is truly done", he said.
"Today will be an important day", he added.
Trump prompted the Nafta revamp more than a year ago, complaining the pact has benefited Mexico to the detriment of U.S. workers and manufacturing.
However, one major stumbling block involving all three countries is the U.S. demand for a so-called "sunset clause", which would oblige the three countries to renew the trade pact every five years.
"We're expecting good news", Castanon said when asked if a breakthrough in negotiations between the USA and Mexico is imminent.
Industry sources believe that 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.
Talks ground to a halt in May, in part due to the July 1 presidential elections in Mexico.
The team of leftist Mexican President-elect Andres Manuel Lopez Obrador has resisted enshrining the 2013-14 opening of the oil and gas sector enacted by the now outgoing President Enrique Pena Nieto in the new NAFTA, people with direct knowledge on the matter said.
Long skeptical of foreign companies entering the Mexican oil industry, Lopez Obrador opposed Pena Nieto's energy reform.