Germany's finance minister has said the EU and U.K. have a "common responsibility" to negotiate a settlement to govern Britain's departure from Europe, but insisted any solution to end the Brexit impasse in the coming days must meet the EU's long-standing list of criteria.

Olaf Scholz said that the current U.K. leader Boris Johnson's recent proposals to break the Brexit deadlock would not be acceptable if they have "an effect on the single market, on the customs union," or if the Good Friday agreement that resolved decades of violence in Northern Ireland might be "endangered." Instead, he said he hoped for a deal that would "follow the lines" of an earlier agreement finalized under former British prime minister Theresa May.

The German finance chief spoke to CNBC as he arrived in Luxembourg to meet his European counterparts, with less than a month until the current Brexit deadline of October 31st, and the possibility of a disorderly departure still a looming threat to several EU nations that have close trading relationships with the U.K.

Earlier this week, a U.K. official in Johnson's office had leaked to select U.K. media outlets the details of a phone call with Scholz's boss, Chancellor Angela Merkel, which indicated that the German leader was deeply dissatisfied with Johnson's desire to keep Northern Ireland out of the European orbit in future. The pound had fallen precipitously Tuesday after alleged details of that phone called were published.

Johnson will meet with his Irish counterpart, Leo Varadkar, in Dublin Thursday. The British and Irish prime ministers remain wide apart on the potential for technological solutions that the U.K. side says will obviate the need for physical customs checks and border infrastructure on the dividing line between the Irish republic and the separate nation of Northern Ireland, part of the United Kingdom.