The EU has named 14 countries whose citizens are deemed "safe" to be let in from 1 July, despite the pandemic - but the US and Brazil are excluded.
Those named include Australia, Canada, Japan, Morocco and South Korea.
EU border controls have been lifted for EU citizens travelling inside the bloc. Rules for UK travellers are covered separately in the Brexit negotiations.
UK nationals are still to be treated in the same way as EU citizens until the end of the Brexit transition period on 31 December. Therefore, during that time UK nationals and their family members are exempt from the temporary travel restriction.
On the current "safe" list, still likely to be amended, are Algeria, Australia, Canada, Georgia, Japan, Montenegro, Morocco, New Zealand, Rwanda, Serbia, South Korea, Thailand, Tunisia and Uruguay.
The UK is currently negotiating "air bridges" with several EU member states, so that coronavirus does not totally block summer holidays - the busiest season in Europe for tourism, which employs millions of people.
The EU procedure to formalise the list, and criteria by which countries are judged safe or not, are to be finalised by midday on Tuesday.
A qualified majority of EU countries - at least 55% of the EU countries, representing 65% of the EU population - have signed off on list.
There were splits between those such as Spain - wanting the boost of tourism, but preferring to play safe because they have been hit so hard by Covid-19 - and others like Greece and Portugal, which depend on tourism but are less scarred by the virus.
Americans are almost certain to be excluded in the short term due to the number of US coronavirus cases.
The number of cases in the United States has surged over the past week, with an all-time high of 45,300 confirmed new daily infections just reached.
Infection rates are high in Brazil, India and Russia, and it’s unlikely the EU will let their citizens in, either. The list would be updated every 14 days, with new countries added and some possibly being left off based on how they manage the spread of the virus.
More than 15 million Americans are estimated to travel to Europe annually, and any delay would be a further blow to virus-ravaged economies and tourism sectors, both in Europe and the United States. Around 10 million Europeans are thought to cross the Atlantic for vacations and business each year.
The European Commission insists that it’s not trying to target any country or that the list might be politicized as tourism-reliant countries around Europe push to get their borders back open again.
“The European Union has an internal process to determine from which countries it would be safe to accept travelers,” spokesman Eric Mamer said Thursday, adding that its decisions are “based on health criteria.”