France is poised to announce on Wednesday that it is dropping its go-it-alone plan to tax big US tech companies in exchange for Washington’s agreement to press ahead with attempts to find a multilateral solution.

Hopes of an agreement were rising in Davos after several days of intense talks involving the French finance minister, Bruno Le Maire, the US treasury secretary, Steve Mnuchin, and Ángel Gurria, the head of the Organisation for Economic Cooperation and Development.

The deal is likely to leave Britain – which will introduce a digital services tax in the spring – more exposed to Washington’s anger over what it sees as attacks on its companies.

Gurria, speaking to the Guardian, said: “There have been a lot of conversations. The exchanges have involved the French showing a willingness to make a move if the Americans do the same.”

The OECD has been working on plans to find an internationally agreed ways of taxing digital commerce and is planning an announcement in the summer.

But some countries have grown impatient with the lack of progress and have decided on unilateral measures. France’s plan – called the GAFA tax because it was seen to target the US companies Google, Apple, Facebook and Amazon – prompted the threat of retaliation from Washington, which vowed to put taxes on French imports, including wine and champagne.

“When you talk about taxing trade it ceases to be a matter for individual countries and becomes an EU question,” Gurria said, warning of an escalation in trade tensions. “Everybody wants to avoid that.”

He added: “If we have an international solution then everybody will adopt it. If we don’t there will be a veritable cacophony of individual national initiatives. Each country will be thinking of a different approach and a different number to apply. We will be back to square one where a number of countries wanted to go their own way.”

Britain is one of the country’s pursuing a go-it-alone approach and will introduce a 2% digital services tax in April.

A Treasury spokesman said: “We are fully engaged in international discussions to address the challenges digitalisation poses for tax. Our strong preference is for an appropriate global solution.

“We’ve committed to introduce our digital services tax from April 2020. It will be repealed once a global solution is in place.”

Mnuchin also made it clear in Davos that Britain, which is seeking to secure a post-Brexit trade agreement with the US, would face tariffs if the chancellor, Sajid Javid, went ahead with the plan.

Gurria said the OECD was still several months away from a multilateral solution to a problem that has vexed policymakers since the rapid growth of digital commerce made it possible for companies to make huge profits while paying little tax.

He said it was important to come up with something more than a lowest common denominator solution. The US is pushing for any OECD-brokered deal to involve only small levies on the Silicon Valley giants, but Gurria said: “If we don’t have something of good quality then that satisfies nobody.”

The French president, Emmanuel Macron, raised hopes of a deal on Monday, when he tweeted he had conducted a “great discussion with Donald Trump on digital tax”.

Macron added: “We will work together on a good agreement to avoid tariff escalation.” Trump replied back with “excellent”.

Gurria said it was encouraging that China and the US had agreed phase one of a trade deal and said a France-US agreement on tax would further improve the mood. He said he had been urging Le Maire and Mnuchin to de-escalate and give the multilateral solution a chance. “I hope that can be confirmed tomorrow”.

The head of the Paris-based OECD – which has 36 developed country members – said he expected Britain and the EU to eventually come up with a trade deal as efficient and least costly as possible.