EU chief Ursula von der Leyen has warned that any deal must not undermine the EU single market, In a downbeat assessment of progress in post-Brexit trade talks.
"We will do all in our power to reach an agreement, we're ready to be creative," she told the European Parliament, warning that Britain must agree to fair trade rules.
"But we are not ready to put into question the integrity of the single market, the main safeguard for European prosperity and wealth," the president of the European Commission said.
She repeated Brussels' warning that Britain will not enjoy the benefits of EU membership from the outside: "There will be a clear difference between being a full member of the Union, and being just a valued partner."
Ms Von der Leyen acknowledged MEPs frustration that time is running out for them to be able to debate and ratify any trade deal before Britain leaves the single market on 1 January.
But she warned that British Prime Minister Boris Johnson's tactics had shown the need for clear rules to be agreed.
"We want to know what remedies are available in case one side will deviate in the future because trust is good, but law is better," she said.
"Crucially, in the light of recent experience, a strong governance system is essential to ensure that what has been agreed is actually agreed."
The British government has been resisting signing up to the EU's vision of a post-Brexit "level playing field", with trade penalties if either side diverges from agreed standards.
Mr Johnson has also introduced a draft law to govern the UK internal market that his own government admits would breach promises made in Britain's EU withdrawal treaty.
This has undermined trust in Brussels, and talks have now blown past several unofficial deadlines, leaving only a narrow window for agreement before the end of the year.
If a deal cannot be signed and ratified by 31 December, cross-Channel trade will face a tariff barrier and businesses on both sides - but especially, experts agree, in Britain - will suffer.
Ms Von der Leyen paid tribute to her chief negotiator Michel Barnier, who tomorrow is due to come out of isolation imposed after a member of his team contracted the coronavirus.
He is then due to return to London to resume face-to-face negotiations with his British opposite number, David Frost. Talks have been continuing by video link.
The main areas of disagreement remain on fishing rights, the level-playing field and the powers of the overall governance mechanism of the eventual accord.
Here, Ms Von der Leyen re-stated the long-standing EU position, but in sterner than usual terms, reflecting the mounting concern among her parliamentary audience that time has run out.
"No one questions the UK's sovereignty in its own waters. But we ask for predictability and guarantees for fishermen and fisherwomen, who have been sailing in these waters for decades, if not centuries," she said.
"Honourable members, as I said, the next days are going to be decisive. The European Union is well prepared for a no deal scenario. But of course we prefer to have an agreement."
All scenarios under consideration ahead of Brexit transition deadline - NI minister
All scenarios are being extensively considered as the deadline for sealing a Brexit transition deal looms, the UK government has said.
Contingencies around Northern Ireland have been given a lot of thought but the priority is securing a deal with the EU by the end of the year, Northern Ireland Office minister Robin Walker said.
Cross-border co-operation on policing, security and criminal justice is a major factor for the authorities.
Mr Walker said: "We are thinking about contingencies, we are thinking about what might be necessary in the event that we have not been able to achieve the preferred outcome from the negotiations.
"Our focus should be on achieving that mutually beneficial outcome.
"A lot of thought has been given to what we will need to do in all scenarios."
Mr Walker was giving evidence to the Northern Ireland Affairs Committee of MPs at Westminster, addressing the extradition of suspected criminals across the Irish border and any alternative mechanisms.
Senior Northern Ireland Office official Mark Larmour said there was good cooperation between the authorities in tackling organised crime, adding: "We have some confidence around the working relationship."