Negotiators are set to work toward an agreement in the coming weeks as the countries seek to resolve their bitter trade dispute just days before the US midterm elections.
Trump subsequently said both sides had "the concept" of a mutually beneficial deal.
Carney said the conversation built on recent discussions about the outlines of a deal that would create jobs, lower costs for families and protect Canada's languages, culture and sovereignty.
"Our teams will now be working in the coming weeks to deliver that outcome," Carney wrote on X on Sunday.
Hours later, after landing in Iowa for a rally, Trump said confirmed the conversation.
"We have the concept of a very good deal with Canada," he said.
"We've been losing money for many years with Canada," he said.
"So we have - we are now very close to having a deal."
The US president mentioned speaking with Carney on Saturday and said the possible agreement is "going to be great for our farmers, great for our country, and it'll be fine for Canada".
Trump said the negotiations involved construction of the Keystone XL pipeline and prospects that the agreement could erase tariffs paid by US farmers for Canadian products.
"Part of the agreement is that our farmers will have to pay no tariffs," he said, even though his comments also made clear that final details had not yet been established.
Still, the upbeat assessment from both leaders was a shift from August, when Canada walked away from negotiations after rejecting US demands that Carney said threatened Canadian sovereignty, French-language protections and the auto industry.
Trump responded with 50 per cent tariffs on roughly $US20 billion ($A28 billion) in Canadian goods, prompting Canadian retaliation.
As recently as Wednesday, Carney said the countries were not yet in a position to reach an agreement before Tuesday's midterm elections.
The two sides have been discussing possible relief from US tariffs on Canadian steel and automobiles.
Trump's trade war with Canada has become an issue in Tuesday's elections, particularly in Michigan and Maine, where crucial Senate races are taking place. Michigan Republican Senate candidate Mike Rogers has called for an end to the tariff war.
Trump's trade war and repeated threats to make Canada the 51st US state have pushed Carney to reduce Canada's dependence on its southern neighbour.
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