Britain on Tuesday marked the third anniversary of its exit from the European Union.
As part of its Brexit divorce, London agreed that EU rules would continue to apply to the movement of goods into and out of the UK territory of Northern Ireland, effectively putting it in the European Union's single market in that regard.
That is to preserve peace there in line with the 1998 Belfast Agreement, which includes ensuring uninterrupted economic integration between Northern Ireland and EU member Ireland.
But London has since reopened negotiations with Brussels on the arrangement, arguing it undermined goods movement within the UK and the role of loyalist politicians in Northern Ireland's power-sharing government.
Both sides have been holding talks at a technical level for months.
In recent weeks they have taken on an increasingly political tone, with meetings between senior officials from both sides, spurring speculation that differences were narrowing.
Von der Leyen refused to say how close the positions were.
"I cannot give partial elements because you never know until the very end how the package looks like, but as I said, these are very constructive talks," she said.
Britain is demanding a lighter touch from the EU on checks of goods entering Northern Ireland from other parts of the United Kingdom.
It also wants the role of the EU's European Court of Justice (ECJ) overseeing the application of EU rules in Northern Ireland for goods to be removed or watered down.