There are also likely to be restrictions on travellers from Brazil and Russia where infection rates remain high.
The EU officials say countries will be on the list depending on the way the spread of the virus is being managed.
Another key condition is whether the country has a ban on citizens from European nations.
EU diplomats confirmed that an official agreement on the criteria - likely to include a limit on the infection rate per 100,000 citizens - is expected on Monday or Tuesday.
The move comes as European countries gradually lift lockdowns imposed place in March to curb the coronavirus pandemic
EU borders to open 1 July
As part of the easing of restrictions, the 27 EU nations and four other countries that are part of Europe’s “Schengen area” - a bloc where goods and people move freely - appear on track to reopen their borders between each other by 1 July.
The list of countries outside the Schengen area proposed at a diplomatic meeting on Friday include Algeria, Australia, Georgia, Japan, Montenegro, Morocco, New Zealand, Rwanda, Serbia, South Korea, Thailand, Tunisia and Uruguay.
The territories of Andorra, Saint-Marin, Monaco and the Vatican are also included.
The European Commission, which monitors the bloc’s laws, believes that travel restrictions should not be lifted for third countries where the situation is worse than the average in the 27 EU member states plus Iceland, Liechtenstein, Norway and Switzerland.
US Covid-19 cases on the rise
The US is not likely to be added to the list due to the surge in the number of cases of Covid-19, with a record high of 45,300 confirmed new daily infections just reached.
The country has reported 124,732 deaths and at least 2.4 million cases overall.
More than 15 million Americans are estimated to travel to Europe annually, and any delay would be a further blow to economies and tourism sectors, both in Europe and the US.
The EU list would be updated every 14 days, officials say, with new countries added and some possibly being left off based on how they manage the spread of the virus.
