The Republican, who has called global warming a hoax, was said to be considering ways to bypass the theoretical four-year procedure for leaving the accord.
The 2015 Paris agreement which went into force on November 4 – just four days before Donald Trump was elected – has gained reaffirmed support from governments ranging from China to small island states to cut greenhouse emissions.
However, the billionaire president has repeated claims there is no evidence that humans are responsible for climate change.
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Trump will be encouraged not to leave the Paris climate deal
He said the Paris deal is "bad for US business" and said the pact allows "foreign bureaucrats control over how much energy we use".
And now European leaders, including Germany, France and Britain, are discussing ways to persuade President Trump not to turn his back on the deal before his advisors meet to discuss its fate on Tuesday.
Western diplomats say they fear a US withdrawal could lead to a “domino effect” and are discussing ways to make their case.
Tusk has attempted to encourage Trump
On Thursday European Council attempted to do just that by using Norway as an example of a state that is tackling climate change and developing renewable energy, while benefiting from fossil fuel exports.
Mr Tusk said: “The Norwegian example should provide encouragement to our American friends, as the climate challenge we all face can only be addressed by common global action,” during a news conference with Norwegian Prime Minister Erna Solberg.
Britain is behind plans to encourage the US not to leave the climate deal
A source told politics news site Politico: “Almost anyone that is aware of this debate and is politically engaged in climate is trying to influence this outcome in any way possible,”
Another official added: “We are trying to clarify that politically, legally, economically, it does make sense for the US to remain.”