"They want to make a deal and we'll see if we can make a deal. We're getting close," Trump told journalists at the G7 summit in Biarritz, following threats to slap tariffs on French wine after Paris voted through a digital tax he has described as "very unfair".
The French parliament passed its new levy in July amid frustration at the slow pace of negotiations to reach a global accord to ensure tech multinationals like Facebook and Google pay a larger share of taxes on their operations.
Britain has also announced plans for a similar tax as criticism grows over tech giants of exploiting fiscal rules to sharply cut their tax bills despite soaring profits.
Under EU law, American tax giants can declare their revenues from across the bloc in a single jurisdiction -- in most cases low-tax jurisdictions such as Ireland or the Netherlands.
But the French move drew accusations of discrimination by Google, Amazon and Facebook -- along with Apple the so-called GAFA companies -- and threats of retaliation by Trump.
The US wants an over-arching agreement on taxation of digital commerce through the Group of 20 economic forum, under the auspices of the Organization of Economic Cooperation and Development (OECD).
In July, G7 finance ministers met for talks at which they reached a consensus on the next steps to take to reach a comprehensive deal by 2020.
Speaking alongside Trump, Merkel reiterated: "We have the intention within the OECD to find a solution for each and everyone by 2020."
"That would be an enormous breakthrough to the benefit of everyone," she said.