The disputed proposal attempts to guarantee that no hard border emerges between EU member Ireland and the UK's province of Northern Ireland in any Brexit scenario.
Barnier on Wednesday poured cold water on that British request, insisting that a comprehensive trade accord could only come by closely abiding by EU rules.
While Downing Street described the meeting as "constructive", the EU side said no proposals had been put forward to replace the Irish backstop.
British Prime Minister Boris Johnson on Monday said there was a "good chance" of striking a Brexit divorce deal with the EU.
The two men are scheduled to hold talks over a lunch of snails and salmon in Luxembourg, amid claims from the U.K. — though not the EU — that a deal is in sight.
"The madder Hulk gets, the stronger Hulk gets and he always escaped, no matter how tightly bound in he seemed to be -- and that is the case for this country," the British PM said.
Cameron revealed he had tried to stop Johnson from joining the Brexit campaign by offering him the post of defence secretary.
In an interview ahead of the publication of his memoir 'For the Record' next week, Cameron said that the victory of the Leave camp in the referendum had left him 'hugely depressed'.
David Cameron said in an interview published Saturday that he thinks about the consequences of the Brexit referendum "every single day" and worries 'desperately' about what will happen next.
The Luxembourg trip is Johnson's latest attempt to meet key European leaders, including the ones from Germany, France and outgoing European Council President Donald Tusk.
In the ongoing five-week suspension of Parliament, MPs are not scheduled to return until October 14, for the traditional Queen's Speech when a new government lays out its agenda for the year.
Johnson has said suspending - or proroguing - Parliament until October 14 is a routine move to allow his government to launch a new legislative agenda.
German Chancellor Angela Merkel has repeatedly expressed concerns that a no-deal exit could deal a body blow to the European economy with a recession already looming.
Parliament was then suspended — or prorogued — at the government's request until Oct. 14, a drastic move that gives Johnson a respite from rebellious lawmakers as he plots his next move.
The backstop is a provision in the withdrawal agreement Theresa May struck with Brussels to keep the Irish border open regardless of the outcome of Britain's future relationship with the EU.