Earlier in the day, Trudeau said it may be possible to reach an agreement ahead of Friday's deadline set by President Donald Trump.
"We recognize that there is a possibility of getting there by Friday, but it is only a possibility, because it will hinge on whether or not there is ultimately a good deal for Canada," Trudeau said at a press conference in northern Ontario. "No NAFTA deal is better than a bad NAFTA deal."
Heyman, who said he has spoken with people in both nations' capitals, said it "looks like we are moving in the right direction."
However, historically there have been certain "no-go zones" for Canada, said Heyman, who served under President Barack Obama from 2014 to 2017.
For one, Canada wants to keep the ability to have a third party settle any disputes. In the revised deal, the U.S. is trying to dump the Chapter 19 dispute resolution mechanism that hinders the U.S. from pursuing anti-dumping and anti-subsidy cases.
Dairy is also an issue, Heyman said. Trump has warned that he expected concessions on Canada's dairy protections.
Canada's dairy farmers operate under a protectionist system that manages supplies and prices, and imposes high tariffs to limit imports. U.S. demands have ranged from ending those tariffs to scrapping a pricing system for milk ingredients that hurt U.S. exports of milk proteins.
Heyman said Trudeau has made it clear that supply management is important.
Trump said Wednesday he was optimistic a deal would be struck that included Canada. The president intends to replace the North American Free Trade Agreement with what he's now calling "The United States-Mexico Trade Agreement."
"I think Canada very much wants to make the deal," Trump told reporters at the White House, while adding, "it probably won't be good at all if they don't."
Canadian trade officials will be negotiating late into the evening, Trump said.
However, if talks break down, Trump and other administration officials have hinted the U.S. would be willing to move forward with Mexico. A preliminary deal between the U.S. and Mexico was announced on Monday.