The two sides are at loggerheads over how to ease post-Brexit trade between Britain and its province of Northern Ireland, with both accusing the other of dealing with part of their divorce deal called the protocol in bad faith.
"We're seeking to urgently come up radical proposals within the protocol to find a way forward," the spokesman told reporters.
"I think it's fair to say they (the issue) may well come up, but the prime minister was clear yesterday that this is not the forum in which he is necessarily seeking to come up with an immediate solution .. Clearly he will want to discuss it with those that raise it with him .. He may choose to raise it himself."
Johnson is due to hold talks at the Group of Seven meeting on Saturday, with France's Emmanuel Macron, Germany's Angela Merkel and the leaders of the European Union.