A resolution would ease long-standing transatlantic friction over imposing taxes on tech multinationals, the largest of which are US-based but operate worldwide.
"We don't yet have an agreement, but we are getting closer in that direction," Mnuchin told reporters.
French lawmakers earlier this year adopted their own digital tax, targeting gross revenues rather than profits, drawing threats from US President Donald Trump to put new tariffs on French wine.
But in August, France agreed to refund taxes collected in excess of a yet-to-be-decided international formula, French Economy Minister Bruno Le Maire told AFP at the time.
The US wants an over-arching agreement on taxation of digital commerce through the Group of 20 economic forum, under the auspices of the OECD.
Under EU law, American tax giants can declare their profits from across the bloc in a single jurisdiction -- in most cases low-tax jurisdictions such as Ireland or the Netherlands.
Britain has also announced plans for a similar tax as criticism grows over tech giants exploiting fiscal rules to sharply cut their tax bills despite soaring profits.