Johnson and the other world leaders are expected to discuss a series of ideas put forward by the UK on Thursday aimed at breaking the current deadlock.
Britain is racing toward its October 31 departure without an exit agreement and faces the threat of economic disruption.
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.
Johnson has suspended parliament for five weeks, with MPs only allowed to return on October 14 -- a fortnight before Britain's planned exit from EU.
Scotland's highest civil court found the suspension was unlawful, but the High Court in England said it was not a matter for judges to intervene in.
The decision outraged many lawmakers, who say it's designed to prevent them from challenging his plan to take Britain out of the EU next month, with or without a divorce deal.
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.
Johnson also repeated the UK government stance for 'calm and restraint' as he stressed that he remains in regular contact with both Indian and Pakistani governments.
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.
Johnson claims he took the action so that he can start afresh on his domestic agenda at a new session of Parliament next month.
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.