The UK and EU are to give updates on efforts to agree a post-Brexit deal following the latest round of talks.
While both sides have previously said a deal is possible, differences remain on issues including fishing rights and post-Brexit competition.
BBC Europe editor Katya Adler says a breakthrough is not expected this week.
The EU has said it would like to agree a deal by October so it can be approved by the European Parliament before the post-Brexit transition period expires.
The transition period ends on 31 December and, if a deal has not been secured by then, the UK would have to trade with the EU on WTO (World Trade Organization) terms.
This means most UK goods would be subject to tariffs until a free trade deal was ready to be brought in.
The UK has said it will not extend talks if an agreement cannot be reached by the December deadline.
EU chief negotiator Michel Barnier met his UK counterpart David Frost on Tuesday evening for dinner, and the pair are expected to have breakfast on Friday morning.
The two sides discussed transport, police co-operation, fishing rights and rules on investment.
The Financial Times reported that Brussels had rejected UK demands to allow British truckers wide-ranging access to the EU.
During the last set of talks in July, Mr Barnier said a deal looked “at this point unlikely” because of the UK’s position on fishing rights and post-Brexit competition rules, known as “level playing field” provisions.
And Mr Frost acknowledged “considerable gaps” remained in these areas, but added that the EU had shown a “pragmatic approach” over UK demands to limit the role of the European Court of Justice after the transition period ended.
He said he still believed a deal could still be reached in September, but the government must “face the possibility” one would not be struck.
Compromises on both sides are inevitable if a deal is to be struck, but don’t expect breakthroughs this week.
For now, much of Europe is still on holiday or dealing with the coronavirus crisis. Boris Johnson is also busy dealing with the fallout from the exams U-turn.
The EU wants a deal, but the keenness for an agreement - even a thin one - doesn’t mean they will settle for a deal at any price.
France is jumpy that Michel Barnier may be so keen to be seen to get a deal done with UK this autumn that he “could be tempted to give away too much”.
Meanwhile, German Chancellor Angela Merkel repeats over and over that the EU won’t agree to anything it believes would damage its single market.
The EU believes Mr Johnson needs to show he can reach a deal, especially after controversy surrounding the government’s initial handling of Covid-19.
But the politics of compromise shouldn’t be underestimated. Compromise can be found - but if it comes it is likely to be last-minute, around October time.
The EU thinks a deal is still more likely than no deal. But only just.