Italian newspaper Repubblica quoted its deputy leader Nigel Dodds as saying the proposal Johnson is said to have made "cannot work, because Northern Ireland has to remain fully part of the United Kingdom customs union".
That is created to prevent the return of customs checks on the island of Ireland, at the border between the British province and EU-member Ireland.
The scheme would see Northern Ireland remain politically in a customs union with the EU but it would be administered by the UK.
Northern Ireland Secretary Julian Smith told BBC Northern Ireland's The View: "We do need to compromise, we do need to focus on coming together and having an accommodation".
A mooted eleventh-hour solution to the deadlock over Brexit can not work because Northern Ireland must remain in a full United Kingdom customs union, the deputy leader of the province's key political party said on Saturday.
According to European Union diplomats, Brussels was willing to enter intense talks with British negotiators this weekend to try to strike a deal after Johnson backed down in key areas, including dropping a demand for customs checks on the island of Ireland.
Speaking after his meeting with the PM, Mr Varadkar said: "I am now absolutely convinced that both Ireland and Britain want there to be an agreement".
British officials have so far remained tight-lipped in the face of the reports.
Instead, he suggested a stronger regulatory border in the Irish Sea, as well as some customs checks on goods moving between Ireland and Northern Ireland.
It comes after an apparent Brexit breakthrough on Thursday when the Prime Minister held crunch talks with his Irish counterpart Leo Varadkar.
Their discussions appeared to unblock the negotiations which had seemed to have been running into the ground following the publication of Mr Johnson's Brexit blueprint.
"In order to secure a sensible deal for everyone it is important that the European Union understand that to maximise the prospects of agreement there will need to be a clear acceptance that the economic and constitutional integrity of the whole of the United Kingdom will have to be respected as we leave".
"A week ago I told Prime Minister Johnson that if there was no such proposal by today, I would announce publicly there are no more chances" of a deal at next week's summit of European Union leaders.