President Donald Trump risks seriously damaging the relationship between Canada and the U.S. as he pushes toward a new North American Free Trade Agreement, former U.S. Ambassador to Canada Bruce Heyman told CNBC on Friday.

"The definition of insanity, just listening to the president there, is how the president has been treating Canada all this time. You know, this is our best trading partner in the world," Heyman said on CNBC's "Squawk on the Street."

After being sidelined from talks for more than two months, Canadian Foreign Minister Chrystia Freeland rushed to Washington, D.C., Wednesday, following Monday's preliminary deal between the U.S. and Mexico. The Trump administration gave Canada a Friday deadline to hash out its differences with the U.S. and join a preliminary, new trade agreement, which serves as a start to replace the 1994 NAFTA among the three nations.

The Trump administration's deadline passed with no agreement. In a news conference late Friday afternoon, Freeland said the two parties will continue to work toward a deal, maintaining that "we're not there yet" on an agreement.

"We know that a win-win-win agreement is within reach," Freeland told reporters. "With goodwill and flexibility on all sides, I know we can get there."

Her comments followed reports from The Toronto Star that Trump privately said he would not make any compromises in trade talks with Canada. Trump later confirmed he had made the comments, writing in a tweet, "At least Canada knows where I stand!"

With an economy 10 times the size of Canada's, the U.S. clearly has all the leverage in these trade negotiations, said Heyman, who served under President Barack Obama from 2014 to 2017. But that doesn't mean the U.S. should use it.

"The U.S. has all the leverage in the world, but just because you can doesn't mean you should. When you take your best friend, your greatest ally in the world, and start squeezing them, you can win, but I will tell you, the relationship will be damaged much longer than it will take the ink to dry on a new NAFTA deal," said Heyman.

As for Mexico's role in all of this, former U.S. Ambassador to Mexico Antonio Garza, who served under President George W. Bush from 2002 to 2009, said he didn't feel the southern neighbor was really at fault.

"I wouldn't say [Mexico] threw Canada under the bus. I think what happened Monday was there was a narrowing of issues, a consensus reached on issues that were particularly difficult in the context of the U.S. and Mexico," Garza said during the same "Squawk on the Street" interview as Heyman.

Mexico may, in fact, view the back-and-forth as a positive step toward an agreement, Garza said. If the three parties reach the point where they can shake hands on a preliminary deal by the end of the day, he added, there will be some wiggle room to work out a final agreement within the next month.

"I think [Mexico is] viewing the back and forth largely as encouraging if it means we are taking steps toward a trilateral agreement," Garza said. "It's only a better agreement if it is a trilateral agreement."

Heyman said a trilateral agreement is the only possible option, and that parties will likely reach some sort of negotiation, but U.S.-Canada relations may be damaged in the process.

"You look at this, and it's not just trade. They were with us in 9/11, like no other country. They were on our side in Afghanistan. They helped diplomats come out of Iran," Heyman said.

"Canada's there, they are going to negotiate that out, but I don't think [Trump's] been treating them too well," he added.

The White House did not immediately respond to CNBC's request for comment.