"We are very very close ... it's fair to say it will be a matter of days", the Canadian source told Reuters News Agency, requesting anonymity given the sensitivity of the situation.
Trade negotiations were halted on Thursday after a member of Michel Barnier's team tested positive for coronavirus. "We are more likely to get a deal than not, purely because the consequences of not getting a deal are so significant and so costly for the United Kingdom and Ireland as it happens, and for some other European Union countries", Coveney told an online conference.
As well as fishing, the other main points of contention are the so-called "level playing field" on competition and the future governance of the deal.
The Prime Minister, for his part, said through a spokesman Tuesday that it was not clear that a deal could be signed at all, especially given the significant rift that persisted between the two sides in a number of key areas.
It was apparently made clear that the two sides are very close to agreement in nearly all areas apart from the three which have long prevented major progress being made. "We are working hard to find solutions which fully respect United Kingdom sovereignty, but it is far from certain that an agreement will prove possible and time is now very short".
With Mr Barnier now in quarantine for up to 10 days, the Monday deadline appears certain to be missed.
"The health of our teams comes first", he said and thanked the European Commission for their help and support.
The positive test raises major questions about how and when face-to-face talks could resume because of the potential need for the negotiating teams to self-isolate.
In London, meanwhile, Prime Minister Boris Johnson was self-isolating in a flat in his Downing Street residence after he had contact with a British lawmaker who later tested positive for COVID-19.
"We have been, and will continue to, act in line with public health guidelines and to ensure the health and welfare our teams".
'We are discussing with them the implications for the negotiations.
The European Union issued Friday one of its most upbeat assessments of the state of post-Brexit trade negotiations, as the talks face an ever tighter deadline for a deal to enter into force for the start of the new year.
"The teams will continue their work in full respect of guidelines", he said. The latest round of talks was taking place in the Belgian capital.
If there is no deal, businesses on both sides of the English Channel will face tariffs and other barriers to trade starting on January 1.
A failure to agree a deal before the end of the transition period will see the two sides forced to trade on World Trade Organisation terms from January 1 and that will mean tariffs being imposed on goods.