The United States, which has the most coronavirus cases in the world and is experiencing a surge in new infections, would be in the same category as No.2 hot spot Brazil and Russia, according to the Times, citing the proposal.
There was no immediate comment from the White House.
Such a ban on U.S. travelers would be a blow to U.S. President Donald Trump, who has blamed more testing for the rise in cases. The pandemic has killed more than 120,000 people in the United States.
Anthony Fauci, the top U.S. infectious disease official, said on Tuesday he was seeing a disturbing surge in several states and pointed to community spread as one reason infections were rising.
In March, when cases were rising in Europe, Trump banned most EU citizens from entering the United States in a bid to curb the outbreak, angering EU officials.
In January, Trump banned entry to the United States of any foreign national who had recently visited China, where the outbreak started late last year.
Once the epicenter of the global outbreak, Europe has brought its infections under control. It has been lifting restrictions and plans to welcome international visitors again in July.
Earlier this month, EU Home Affairs Commissioner Ylva Johansson said the list of countries with allowed visitors would be based on three criteria: countries should have COVID-19 under at least as much control as the EU average, have containment measures during travel and also be willing to let in EU visitors.
(Writing by Lisa Shumaker; Editing by Howard Goller and Franklin Paul)