Earlier Monday on CNBC, Sen. John Barrasso brought up the idea of a scaled-back deal, which he referred to as a "kind of a 'NAFTA light.'"
The Wyoming Republican said the best way forward would be to take Congress out of the equation so an agreement "doesn't have to be ratified."
"If you can work around the edges to improve it for the United States, absolutely do it," said Barrasso, chairman of the Senate Republican Policy Committee, the fourth-ranking post in the GOP leadership hierarchy.
In response to Barrasso, Mnuchin said, "We can easily look at the 'skinny deal' as an alternative and that's something that the president can consider."
Last week, Lighthizer said the parties are "nowhere near close to a deal."
House Speaker Paul Ryan, who is not seeking re-election, had said the Republican-controlled Congress needed to see any deal by last Thursday to give lawmakers a chance to approve it before the new Congress takes over in January.
"For the moment, the president is focused on the agreement that he wants to get between the three countries. And then we'll figure out how to get it through Congress," Mnuchin said Monday.
Trump has repeatedly threatened to pull out of NAFTA if negotiators can't get a better deal.
— CNBC's Matthew J. Belvedere and Reuters contributed to this report.