Citizens from 23 EU countries are eligible to take part in the US visa waiver scheme when they want to travel to the US, but those from Cyprus, Poland, Romania, Bulgaria and Croatia are not.

Canada has a similar programme, which excludes citizens from Romania and Bulgaria.

The EU has the power to sign visa waiver agreements on behalf of its member states, which then apply to all of them. It may also suspend such agreements.

The EU is telling the US and Canada to treat all EU citizens equally, a principle called “full visa reciprocity”.

The long-standing issue is expected to be on the agenda next Tuesday, when EU commissioners meet in Strasbourg.

“A political debate and decision is obviously needed on such an important issue. But there is a real risk that the EU would move towards visas for the two (Americans and Canadians),” an EU source told Reuters.

In the commission's most recent report on the issue, dated 5 November 2015, it said “it is unlikely that all non-reciprocity cases involving Canada and the US will be resolved by April 2016”.

In the report, it noted that it was unlikely that “suspending the visa waiver for certain categories of citizens of these third countries would lead to a change in their legislation/policy framework which would ensure full visa waiver reciprocity”.

But the Reuters quote indicates that the commission's assessment may change.

There are fears that if the EU does move to reintroduce visa requirements for Americans that it may harm negotiations on the free trade and investment treaty known by its acronym TTIP.

Later this month, US president Barack Obama is visiting Europe, and will have talks in the UK and Germany. He is expected to discuss TTIP with UK prime minister David Cameron, and German chancellor Angela Merkel.

The EU reciprocity debate comes amid fears in the US that EU visa perks could help “foreign fighters” infiltrate the US.

The term refers to radicalised EU nationals who went to train with the jihadist group Islamic State in Syria prior to returning home.

The US has already tightened up security measures for visa-waiver states on the back of the concerns.

Dianne Feinstein, a prominent US senator, last year called the waiver scheme America’s “Achilles heel.”