"I believe he is testing Canada, and how we push back to this.Trump is a shrewd businessman and a hard one".
The sources said Trump had not made a final decision on the notification, but it could come within days.
The White House did not immediately return a call for comment.
Trump says he's working to make life easier for working Americans.
That statement will send waves of relief rippling through Ottawa and Mexico City.
The White House has confirmed that the United States is considering pulling out of NAFTA.
Markets appeared jolted by the sudden drama.
Both the Canadian dollar and the Mexican peso rose against the US dollar after the release of the White House statement.
Since launching his bid for president, Trump has repeatedly criticized the nation's trade deals, especially NAFTA, saying the agreement signed in 1994 has been a "disaster" and allowed many U.S.jobs to shift to Mexico. If they are willing to make it easier for American families to own a home, why is Washington complaining?
But many Republicans on Capitol Hill have expressed concerns about Trump's hardline on free trade deals.
Politico and CNN, both citing unnamed White House officials, said the order has been drafted but not yet finalized.
U.S. Commerce Department officials say it's been a tough week for trade relations with Canada. "NAFTA truly opened the door to the strong and growing market opportunity in Mexico".More news: Congress scrambles to wrap up deal averting govt shutdown
Priebus says Trump is "showing some reasonableness on the wall and border security", a move that has put Democrats "on their heels".
"It would be a nothing".
A disruption in trade between the three NAFTA partners could wreak havoc in the auto sector and other industries, hitting profits at companies that have benefited from zero-level tariffs and Mexico's relatively low labor costs.
He pointed out that NAFTA does not have an automatic-exit clause.
If Trump chose to withdraw completely from NAFTA, it would have "profoundly negative consequences" for Texans and for the country, Cornyn added.
National Corn Growers Association President Wesley Spurlock said, "Mr. President, America's corn farmers helped elect you".
Froman said the negotiations petered out after the election, when "some on the Canadian side, whether it was the government or whether it was the industry", preferred to take their chances with Trump.
During his run for office past year, Trump made his disdain for NAFTA a central component of a populist message created to engender support among working class Americans.
But Manitoba Conservative MP Robert Sopuck, who represents the Dauphin-Swan River-Neepawa riding, said the argument that Canadian softwood lumber is subsidized and therefore cheaper than US lumber is "nonsense".
"It's been frustratingly slow, " Ross said earlier this month, of Congress. "And one thing we've seen from this administration is they are really, when they get a bit in their mouth on some of these issues, they will run with it". "That's been not helpful".