The Financial Times said the change, which will also apply to EU citizens, would mark the end of the 18-month blanket ban imposed by Donald Trump and maintained by Joe Biden.
The FT said fully vaccinated passengers would be able to travel once the ban is lifted within weeks.
UPDATE: US to lift UK and EU travel ban in November
Currently, only US citizens, immediate family, green card holders and those with exemptions can enter the US if they have been in the UK or EU in the previous fortnight.