EU chief Ursula von der Leyen raised the prospect a day before Canadian leader Mark Carney was due to address the European Parliament.
Her pitch comes as both Canada and the European Union seek to pivot away from an aggressive United States under Trump's leadership.
"I think it's laughable," Trump told reporters when asked about the plan.
"If they do that, if I think it's at all a hostile act, I will put very serious tariffs or stop trading with Europe, on many things."
He added: "If it's a good intention, that's fine. If it's a bad intention, we'll put very heavy tariffs on Europe, which is a possibility."
Von der Leyen pitched closer cooperation on tech, defense and energy to Carney, who became the first non-European head of government to attend the annual "State of the European Union" speech.
The German told the European Parliament in Strasbourg that, as democracies face a "fracture in the international rules-based system," Brussels and Ottawa needed to pull closer together.
"I would like to work with you on opening the door for Canada to be the first associate member of the EU," von der Leyen told the Canadian premier, drawing a standing ovation in the chamber.
Canada's Carney seeking closer EU ties, to attend State of the EU address
A broader alliance
Carney has been pursuing closer ties with the European Union as Canada gets drawn ever deeper into a trade war with the United States.
He is set to address the parliament on Thursday, with his visit meant to act as a catalyst ahead of an EU-Canada summit in Montreal next month.
Von der Leyen said it was time to move from cooperation based on trade to a broader "alliance for the future" and "bring the relationship with Canada to the highest level possible."
"We will work on intelligent manufacturing. We will create a tech alliance. We will integrate defense industrial bases. We will make the Arctic a flagship joint project," she said.
She listed energy, critical minerals, batteries, AI, cyber and economic security as other fields of cooperation.
"This is a partnership not against anyone else, but for our common strength," she said.
But both the EU and Canada have been buffeted by tariffs and territorial threats from the US and competition from China.
"In a more dangerous and divided world, Canada is forging stronger relationships with trusted partners," Carney's office said in a statement.
EU chief unveils €200m Greenland package amid tensions over Trump claims
What's in a name
While EU treaties do not envision the possibility of becoming an "associate member," the idea was first floated by German Chancellor Friedrich Merz this year for Ukraine.
Under that plan, which met a cold reception from a country pushing for full membership, Ukraine would have been allowed to attend the bloc's summits and have a representative in the European Commission.
It would have also benefited from parts of the EU budget, but without full voting rights.
"We don't really know yet what it means," said Tobias Cremer, a center-left European lawmaker from Germany and the main sponsor of a resolution urging stronger EU-Canada cooperation, after von der Leyen's "associate membership" pitch.
Under EU rules, member states have to approve any form of partnership with a third country and it was unclear how much support von der Leyen's proposal would receive from capitals.
Brussels and Ottawa already enjoy a considerable level of cooperation.
The CETA free-trade agreement that abolished almost all tariffs has been credited with boosting trade in goods and services by more than 80 percent since 2016.
And this year Canada became the first non-EU country to join a flagship defense loan programme.
Carney later flew to Britain for his first meeting with new UK Prime Minister Andy Burnham.
They attended a football match between Everton and Wolverhampton together before Carney's return to Strasbourg for his Thursday speech.



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