Johnson will discuss the so-called "Landing Zone" agreement for Northern Ireland with EU leaders including German Chancellor Angela Merkel, French President Emmanuel Macron and European Commission president Jean-Claude Juncker by the end of Monday, The Times reported.
UK-based media dubbed the upcoming Johnson offer as a "historic grand bargain on Brexit", which reportedly would help deliver his new blueprint this week or finally agree on a no-deal withdrawal by the slated for 31 October deadline.
According to sources cited by The Times, Johnson is mulling enlisting the EU leaders to press chief Brussels negotiator Michel Barnier to agree on the details of the UK PM's Brexit plan.
UK-EU talks on the withdrawal deal have seen months pass with no breakthrough. On Friday, Brussels said the sides would intensify negotiations in the coming days.
Johnson has been seeking to withdraw the United Kingdom from the European Union either with a deal or without. UK lawmakers are almost uniformly vehemently opposed to Johnson's methods and goal.
Earlier, UK-based media broke the news suggesting that Johnson might use "Super Saturday" to receive approval from both the lower and the upper houses for his Brexit deal before the October deadline.
The UK government will reportedly ask the House of Commons to sit on "Super Saturday", 19 October, for the first time since the 1982 Falklands crisis, in a bid to push through any deal Johnson brings from the European Council summit, scheduled for 17-18 October.
Last week, Johnson unveiled his new Brexit blueprint which revolves around an all-Ireland regulatory framework on cross-border trade. Under his plan, Northern Ireland would exit the EU customs union with the rest of the UK after the end of the transition period, albeit with some form of regulatory checks in place for goods crossing the Irish Sea from the British mainland to the six counties.
Despite his determination to take the country out of the bloc, Parliament has obligated him to seek an extension if no agreement is secured by the deadline.
Earlier, the Commons passed legislation - the so-called Benn Act - requiring the prime minister to ask the European Union for a deadline extension if either the withdrawal agreement or a no-deal option is not endorsed by UK lawmakers on or by 19 October.
Johnson could also use "Super Saturday" to scrap the Benn Act or, in the case of a no-deal with the EU, to initiate a vote on further steps which could include a second referendum or a complete revocation of Brexit.