Johnson and von der Leyen are pressing to break a logjam over fishing rights with just nine days to go before Britain leaves the EU single market and customs union.
An EU official, who declined to be named, said disagreements over fisheries were not yet resolved, and many more minor issues still required "polishing".
The pound is benefiting from an improvement in the narrative on the chances of a Brexit trade deal this week, almost a year after Britain formally left the European Union.
The EU's chief executive said on Wednesday she could not say if there would be a trade deal with Britain but there had been progress and the next few days would be critical.
"The next days are going to be decisive," the president of the European Commission told the European Parliament, as intense talks on a post-Brexit trade deal continued nearby in Brussels.
Leaders were looking to salvage the EU's 1.8-trillion-euro ($2.1-trillion) budget and coronavirus recovery package, seen as vital for the continent's battered economies, after it was blocked by Hungary and Poland over provisions linking it to the respect for rule of law.
Hopes US lawmakers could be close to a breakthrough in deadlocked talks helped fire a rally across Asian markets Wednesday after the White House proposed an economic rescue package that was bigger than a bipartisan plan put forward last week.
The agreement largely replicates an existing EU-Singapore pact, with the city-state saying it will cover more than 17 billion pounds (US$22 billion) in trade.
The EU and Britain had cast Thursday's meeting as a chance to break an impasse in negotiations but both acknowledged there was a danger that a trade deal would elude them.
Gove cautioned that it could not be a deal at any price and that the EU needed to both make concessions and understand that the United Kingdom was sovereign for there to be a deal.
The blue-chip FTSE 100 was up 0.3% by 0802 GMT, led by financial, energy and consumer discretionary stocks, as Asian shares hit a record high following positive vaccine news.
"Tomorrow is pivotal," Coveney told Irish national broadcaster RTE, referring to a meeting on Wednesday between British Prime Minister Boris Johnson and European Commission President Ursula von der Leyen.
"Broad positioning is short sterling, but not at extremes by any means. This limits the prospect we get an exaggerated short-covering rally to say $1.3800 or $1.4000."