EU chief negotiator Michel Barnier has signalled a willingness to be flexible in Brexit negotiations around the Irish border.
Fears of a return to violence have been raised if the Good Friday Agreement is damaged by the imposition of a hard border on the island of Ireland after Brexit.
The EU's suggested solution to the problem - a common regulatory area for goods and customs with the rest of the EU - has so far been rejected by the UK as "annexing" Northern Ireland.
Calling the issue "the biggest risk" caused by Brexit, Mr Barnier said he was "ready to improve" the EU's proposal.
He said: "Since we will not know what the future relationship will bring by autumn 2018, we need to have a backstop solution in the withdrawal agreement.
"The UK agrees with this, and both the EU and the UK have said that a better solution in the future relationship could replace the backstop.
"What the EU has proposed is that Northern Ireland remains in a common regulatory area for goods and customs with the rest of the EU.
"We are ready to improve the text of our proposal with the UK."
Mr Barnier was also positive about reaching a deal "unprecedented in scope and depth" around free trade.
He warned that UK proposals must not "undermine" the four pillars of the single market - free movement of goods, capital, services and labour, which he called "one of the EU's biggest achievements" - by seeking freedom only for goods.
"But I remain confident that the negotiations can reach a good outcome," he said.
"It is possible to respect EU principles and create a new and ambitious partnership."
