German Chancellor Angela Merkel told British Prime Minister Boris Johnson on Tuesday that his Brexit plan was doomed to fail without further compromise on the Irish border issue, a Downing Street source said.

In a phone call, Merkel warned the British leader that a deal was "overwhelmingly unlikely" unless he dropped his opposition to keeping British-run Northern Ireland in the European Union's customs union.

But Johnson has repeatedly said he will not shift on the issue, pointing to a collapse in the negotiations just weeks before Britain's scheduled EU exit on October 31.

According to the BBC, the prime minister's office believes talks are now "close to breaking down".

In Berlin, a spokesman for the German government confirmed to AFP the two leaders had spoken but said he would not comment on the content of the call.

Johnson unveiled a new plan last week aimed at keeping Britain's border with EU member Ireland free-flowing after Brexit - a crucial issue in the divorce talks between Brussels and London.

It envisages keeping Northern Ireland aligned with the EU's single market regulations, but part of a UK-wide customs territory.

But this would mean customs checks on the Irish border, something the EU has long opposed.