The private meeting will allow the leaders to have what are described by Downing Street as 'detailed discussions' about the process for securing a Brexit agreement
Irish sources are less upbeat. If they do not secure changes, then attempts to get a deal could be formally shut down by the weekend.
The Liverpool Echo has reported speculation that Liverpool will host the meeting as a sort of neutral venue.
Both leaders will be accompanied by senior officials for the talks and Mr Barnier's team in Brussels will be kept fully informed.
Mr Johnson has vowed Britain will leave on 31 October with or without a deal, despite MPs passing a law last month that requires him to seek another Brexit delay if he fails to secure a pact at the summit.
But Mr Barnier struck a downbeat tone yesterday, telling the European Parliament that "we're not on the point of envisioning and finding a deal".Read more: RTÉ News
Varadkar and Johnson talk by phone and reiterate desire to reach Brexit deal Leo Varadkar : 'I don’t play dirty, I don’t think most EU leaders do either' Bollocks, his lies have now been exposed, the backstab was a trap that gave Dublin a veto over the United Kingdom until they ripped up the Belfast Agreement to shreds and coerced Northern Ireland out of the UK or made us a colony of Dublin NoAnnexation NoSurrender really? Your leadership campaign would tell a different story Teesh
Varadkar to travel to Liverpool for make-or-break Brexit showdown with JohnsonTaoiseach Leo Varadkar is to travel to Liverpool on Friday for a make-or-break showdown meeting with British Prime Minster Boris Johnson . where will be the venue in Liverpool wld it be a hotel as a 'neutral' venue? Ummm.. 'make-or-break' 'showdown' What is this, reality TV? And of course it's neither make or break or a showdown.
Varadkar to travel to England for make-or-break Brexit showdown with JohnsonTaoiseach Leo Varadkar is to travel to Liverpool on Friday for a make-or-break showdown meeting with British Prime Minster Boris Johnson .