The deal is said to involve more US access to Canada's dairy market and a cap on Canada's car exports to the US.
Nafta governs more than $1tr (£767 bn) in trade between the two and Mexico.
Mexico and the US have already agreed new terms, and only recently it looked as if Canada could be excluded in a final agreement.
A protectionist policy under the US President Donald Trump has seen the US forge ahead with individual trade deals, rejecting bigger multi-lateral trade agreements and posing a challenge to decades of global free trade.
Mr Trump earlier this year imposed taxes on imports from Mexico and Canada - and the two countries retaliated.
The Trump administration set Sunday as a deadline for Canada to strike a deal.