The European Union's chief Brexit negotiator says reaching a deal on Britain's departure from the bloc before the scheduled date of October 31 has become "more and more difficult", and Finland's EU minister says leaders will discuss another delay.
The EU's Michel Barnier added, however, that a deal is still possible this week.
But EU ministers expressed more scepticism as they gathered in Luxembourg for the last preparatory meeting before a summit of national leaders in Brussels on Thursday and Friday.
The main sticking point is customs and security arrangements for the border between EU member Ireland and the British province of Northern Ireland, the only land frontier between the EU and the United Kingdom after Brexit.
"Even if an agreement has been difficult, more and more difficult, it's still possible this week," Barnier told reporters on arriving in Luxembourg.
"Reaching an agreement is still possible. Obviously, any agreement must work for all. The whole of the UK and the whole of the EU. Let me add also that it is high time to turn good intentions in a legal text."
Finland's EU affairs minister, Tytti Tuppurainen, said the EU must prepare for a no-deal and another extension of the tortuous divorce process.
"All scenarios are open," she said, adding that leaders at the summit would discuss pushing back the departure date beyond October 31.
British Prime Minister Boris Johnson, a leading figure in the 2016 referendum in which Britons opted to leave the EU, has pledged to take the United Kingdom out of the bloc on that day whether or not a withdrawal agreement has been reached.
But the British parliament has passed a law saying the country cannot leave without an agreement, and Johnson has not explained how he can get around that.
Malta's EU minister, asked if he would bet on there being a Brexit deal this month, said: "I would not."
German EU minister Michael Roth echoed that sentiment, saying he was not "quite sure if a deal is close".
"Nobody wants a hard, disorderly Brexit but that's what we're heading for. There are still a few short days to reach a solution that's sensible for all concerned," he told reporters.
"The EU's conditions are very, very modest. The single market cannot be infringed and we want continued peace in Ireland and Northern Ireland."
As they met, British Brexit negotiator David Frost was starting another round of negotiations with the EU's executive European Commission in Brussels on Tuesday.
A British government source said separately that new texts have been shared repeatedly with Brussels during talks.
The main sticking point is around customs, with London proposing that Northern Ireland stays in the UK customs area but that EU tariffs are applied on all goods crossing from mainland Britain to the island.
Businesses would be eligible for a refund if it turns out their goods stay in Northern Ireland under the plan, which the EU has many doubts about, saying the system is too complicated, untested and not detailed enough at this stage.
The EU believes the only possible deal to be had at the summit is a return to a solution - already rejected by Britain previously - of keeping Northern Ireland in the bloc's customs union.
It would require a major shift from London and Johnson will face his factious parliament at a rare Saturday session after the summit.