A formal announcement is expected by Saturday, they said.
The news spurred investors to boost positions in tariff-sensitive firms, aiding a recovery among a swathe of European stocks.
The pan-European STOXX 600 index rose 0.5%, buoyed by a 2% gain in shares of tariff-sensitive auto makers and their suppliers, with BMW tacking on 3.1%.
The broad benchmark had fallen as much as 0.7% earlier in the day, while auto stocks had plumbed a 1-1/2 month trough, down 2.1%.
Atlantic Markets' John Woolfitt said it appeared the market was relieved that Trump "can actually act in a civilised manner and isn't on a total rampage inciting trade wars across the globe," giving the partnership and relationship with the EU "some much needed respite".
"Whilst he is entangled in the ongoing dispute with China, it gives the impression he is reluctant to travel down the same road with the EU."
Frankfurt's auto-heavy DAX and London's FTSE 100 rose 0.9% and 0.8%, respectively, while their Milan-traded peers dipped 0.1% on weakness among the country's banks.
Shares of Italian lenders have been pressured this week, as yields on the sovereign's bonds continue to rise a day after Deputy Prime Minister Matteo Salvini said Rome was ready to break EU fiscal rules.
"Pressure on Italy is mounting ... the doom loop, linking the banks to the sovereign, remains strong," said Marc C. Chandler, chief market strategist at Bannockburn Global Forex.
Italy's banks could come to the rescue of Carige to safeguard financial stability after BlackRock dropped a planned bid for the struggling regional lender, UniCredit's chairman said.
However, the chief executive of Italy's top retail bank, Intesa Sanpaolo, said it would not put any more money into an industry fund which could rescue Carige.
On the whole, European banks dipped 0.1%, weighed down by some disappointing earnings.
Some investors exited positions in Austria's Raiffeisen Bank International (RBI) and French lender Credit Agricole as first quarter profit figures disappointed, sending their shares 3.7% and 2.6% lower, respectively.
London-listed CYBG Plc bucked the trend among lenders, rising 3.3% after swinging to a first-half profit.
Thyssenkrupp dived 5%, nearing the price it opened at on Friday, when short-sellers rushed to cover their bearish exposure after the industrial conglomerate announced plans to spin-off its elevator business.
E.ON tumbled 5.8%, after Goldman Sachs downgraded the energy company's stock, which was also trading ex-dividend.
(Reporting by Medha Singh and Aaron Saldanha in Bengaluru; Editing by Alison Williams)
By Medha Singh and Aaron Saldanha