"We may do 2A and some of the tariffs come off. We can do this sequentially along the way," he added.
Mnuchin's warning to Italy and Britain comes after France backed out and pledged with the U.S. to avoid a trade war until at least the end of this year.
British Prime Minister Boris Johnson in December had pledged to make major multinational companies pay their fair share of tax, including the implementation of a Digital Services Tax.
Italy approved a similar tax in the 2019 budget but it has not activated it yet.
Mnuchin said that he hoped Britain and Italy would suspend their plans to impose the taxes, according to the report.
"If not they'll find themselves faced with President Trump's tariffs. We'll be having similar conversations with them."