Mr Trump has been highly critical of the 2015 accord, under which Iran limited its nuclear activities.
EU powers see it as the best way to stop Iran developing a nuclear bomb and their officials met a senior Iranian on Tuesday without US officials present.
The White House has signalled that the president might stop short of reneging completely on the deal.
It is unclear what that would entail. The president's announcement will take place at 14:00 (18:00 GMT) on Tuesday
UK Foreign Secretary Boris Johnson urged Mr Trump not to "throw the baby out with the bathwater" on Monday, while his French counterpart Jean-Yves Le Drian made clear that France, the UK and Germany would continue to honour the accord.
Iran's President Hassan Rouhani has warned that his country could face "some problems" in the coming months, but stressed it will "keep working with the world".
Envoys of Germany, France and the UK discussed the situation with Iran's Deputy Foreign Minister Abbas Araghchi in Brussels on Tuesday, an EU statement said.
An unnamed German official told Reuters news agency that representatives of the countries had been in contact for weeks.
"In the coming days, it will also be important to remain in discussion with all sides to avoid an uncontrolled escalation," the official said.
What was agreed under the deal?
The so-called Joint Comprehensive Plan of Action (JCPOA) saw Iran agree to limit the size of its stockpile of enriched uranium - which is used to make reactor fuel, but also nuclear weapons - for 15 years and the number of centrifuges installed to enrich uranium for 10 years.
Iran also agreed to modify a heavy water facility so it could not produce plutonium suitable for a bomb.
In return, sanctions imposed by the UN, US and EU that had crippled Iran's economy were lifted.
The deal was agreed between Iran and the five permanent members of the UN Security Council - the US, UK, France, China and Russia - plus Germany.
Iran insists its nuclear programme is entirely peaceful, and its compliance with the deal has been verified by the International Atomic Energy Agency (IAEA).
He complained that the deal only limited Iran's nuclear activities for a fixed period; had failed to stop the development of ballistic missiles; and had handed Iran a $100bn (£74bn) windfall that it used "as a slush fund for weapons, terror, and oppression" across the Middle East.
European leaders attempted to persuade Mr Trump that his concerns could be addressed through a supplemental agreement.
What could Mr Trump announce?
The president could immediately hit Tehran with a barrage of oil and banking sanctions, along with measures targeting Iranian companies - a hard. Nick Bryant in Washington says could effectively kill the entire deal.
What has Iran said?
President Rouhani told an audience of oil and gas executives in Tehran on Tuesday morning that if Mr Trump chose to reimpose sanctions, Iran would "face some problems for two or three months" but would "pass through this".
He stressed that "the foundation of our policy is to work and have constructive relations with the world" - an apparent reference to other parties to the deal.
But others within his government struck a different tone.
It "will not be in the Americans' interest" if they cause the deal to collapse, the secretary of Iran's Supreme National Security Council said.
Iran "will not be passive if the US starts confrontation" with it, Fars news agency also quoted Ali Shamkhani as saying.
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