Theresa May is heading to Brussels to speak to EU leaders as she battles to keep hopes of a Brexit deal alive.
Expectations of a breakthrough are low, with talks deadlocked over the Irish border issue.
EU leaders say it is up to the UK prime minister to come up with fresh ideas to solve it.
Mrs May is sticking to the plan she has already set out – but there is speculation the post-Brexit transition period could be extended.
This European Council meeting was meant to be the occasion when the remaining 27 EU member states gave the green light for a special summit in November to finalise the terms of Britain’s withdrawal from the EU.
Both sides want to get an agreement in place within the next few weeks to avoid the prospect of the UK leaving without a deal on 29 March.
But chief Brexit negotiator Michel Barnier is expected to say talks have failed to make the “decisive progress” the EU wanted to see before agreeing to a special summit.
Ireland’s Deputy Prime Minister Simon Coveney said: “I think what’s more likely is that dates will be suggested, but that there won’t be a commitment to a new summit unless there is a signal from the negotiating teams that there is something to sign off on.
“And I think that’s sensible. What we don’t want to do is create drama around the build-up to a new summit date and not actually have something to sign off on.”
There is also speculation some EU leaders will suggest using a November summit for a no-deal planning session instead.
Mrs May will address her fellow leaders on Wednesday evening, and, before that, will hold one-on-one talks with EU chiefs Donald Tusk and Jean-Claude Juncker, as well as Irish premiere Leo Varadkar.
But she will leave before the meal where the EU leaders decide what to do next.
Mr Tusk, president of the European Council, said on Tuesday he saw “no grounds for optimism” that the two sides could bridge their differences on the Irish border, but appealed for “goodwill and determination” to try and bring an agreement nearer.
The border between Northern Ireland and the Republic of Ireland will become the border between the UK and the EU when the UK leaves the EU.
Both sides want to avoid that border having checkpoints or other physical infrastructure to carry out checks on goods, but they can’t agree how that should be done.
They are discussing a “backstop” – a position of last resort, to protect an open border on the island of Ireland in the event that the UK leaves the EU without securing an all-encompassing deal.
The EU’s suggestion would see Northern Ireland remaining in the EU customs union, large parts of the single market and the EU VAT system, but Mrs May says that would effectively create a border between Northern Ireland and the rest of the United Kingdom.
She suggested a backstop that would see the UK as a whole remaining aligned with the EU customs union for a limited time after 2020.
The EU also says any backstop plan should not have an end date – something Mrs May has previously insisted on, leading to the possibility of a “backstop to the backstop”.
The UK and EU negotiators have, separately, discussed extending the 21-month transition period by up to a year, to improve the chances of getting a full trade deal and reduce the chance of needing an Irish border backstop.
Extending the transition period has never been ruled out by the UK government, but it is unlikely to be acceptable to Conservative Brexiteers.
Downing Street has said they are not calling for an extension.—BBC