The EU side have accepted a proposal to have a transition period on fishing rights in the new year. However, there has so far been no agreement on when the period should end or how it will work.
The fishing transition period would allow the UK to catch its increased quota.
It would also give the EU more time to prepare for receiving a smaller share of the fish from British waters.
Government figures reportedly think this compromise is a sign that the EU will give in to other demands from the UK on fishing in the next week of intensive talks in London.
The EU’s chief negotiator, Michel Barnier, arrived in London on Friday ahead of the negotiations.
Before his arrival, Mr Barnier wrote on Twitter that the “same significant divergences persist” in Brexit talks.
His UK counterpart, Lord David Frost, also took to Twitter on Friday to admit “it is late” to be negotiating for a deal.
However, Lord Frost added: “A deal is still possible, and I will continue to talk until it’s clear that it isn’t.
“But for a deal to be possible it must fully respect UK sovereignty.
“That is not just a word – it has practical consequences. That includes: controlling our borders; deciding ourselves on a robust and principled subsidy control system; and controlling our fishing waters.
“We are working off the same grid but there is no agreement on what should be in the grid and we could still end up ditching the grid.”
In September, Lord Frost proposed a transition period of up to three years.
But the EU reportedly want a much longer period.
Sources have estimated that the EU are demanding at least ten years, according to The Telegraph.
Fisheries arrangements between the UK and EU for after 1 January have been one of the largest barriers in Brexit trade deal talks.
On Monday, Irish Prime Minister Micheal Martin said he was “hopeful” the outline of a deal could be agreed by the end of this week.
The UK will continue to follow the bloc’s rules until the end of the year as part of the current transition period.
But if a trade deal is not agreed before the end of the period, trading between the EU and UK will default to the World Trade Organization (WTO) rules.
The two sides can continue negotiating next year if a deal is not agreed, however both would face import taxes on goods traded between them.