The proposed three per cent technology levy would target multinational companies with global revenues of more than £660m a year, in a move that could raise £4.4bn a year across Europe.
Bruno Le Maire told French radio station France Inter Radio: “We are close to having a deal in our hands.”
Some smaller member states have expressed uncertainty over the European Commission’s proposal over fears of lost revenue, and German finance minister Olaf Scholz said it was important to find time for a thorough debate on the plans.
However, the European Commission is pushing for a deal by Christmas.
The body’s head of tax told the BBC that an agreement was “doable by Christmas” and “let’s do it now.”
Last month, chancellor Philip Hammond announced plans for a two per cent UK digital services tax in the Autumn Budget, which would hit profitable businesses within the tax’s scope, such as search engines, social media platforms, and online marketplaces that earn at least £500m in global revenue.
Hammond said the move - which will be consulted on ahead of an April 2020 start date - is to ensure “the UK continues to be the best place in the world to start and scale up a tech business", however the technology sector hit back at the plans.
Wandisco co-founder and chief executive David Richards warned that “in the longer term, heavy-handed policy will feed the climate of uncertainty that surrounds the UK and encourage and isolationist mentality that damages Britain post-Brexit.”
Russ Shaw, founder of Tech London Advocates, added: “Tackling the digital tax question without coordinating efforts with the US and EU as key global partners, will only further entrench Britain in an isolationist position we can not afford.”