Theresa May could travel to Strasbourg later today in a last-ditch effort to break the Brexit impasse.
Tánaiste Simon Coveney said it's his understanding that the British Prime Minister will "try to finalise an agreement... if that's possible" with Jean-Claude Juncker.
It comes ahead of tomorrow's second 'meaningful vote' in the House of Commons on the Brexit deal.
Mrs May and Mr Juncker have already spoken by phone, and talks between the EU and UK negotiating teams are continuing.
Earlier, both EU and British officials confirmed talks were deadlocked.
The British government has been trying to secure concessions from the EU over the backstop to avoid a hard border in Ireland.
However, Downing Street has admitted that negotiations remain at an impasse.
Tomorrow, MPs will have a second 'meaningful vote' on Theresa May's Brexit deal, following its historic defeat in the House of Commons in January.
The first vote was the largest defeat for any government in modern UK parliamentary history.
If it's defeated again, politicians will be asked whether they reject exiting the EU without a deal.
If that's also rejected, MPs will be asked to vote on whether they approve of a short extension to Brexit.
This week's votes come just over two weeks before the UK's due to leave the EU on March 29th.
Speaking this afternoon, Minister Coveney said: "Negotiations are ongoing. Many had hoped we would have clarity at this stage - particularly in advance of the vote tomorrow. We don't, yet.
"I don't think it's helpful to go into detail of what the obstacles are to getting an agreement - there are some.
He added: "Our approach remains the same: we're very clear that the withdrawal agreement can't change in terms of text, but we also want to try and be helpful in terms of providing the clarity and reassurance needed in Westminister.
"Nobody's looking to trap anybody anywhere permanently - but the backstop needs to be there."
'No breakthrough'
Speaking on Breakfast Briefing this morning, Euronews UK Correspondent Vincent McAviney said so far the negotiations in Brussels have failed to lead to any breakthrough.
He said: "Many people are now predicting that the defeat tomorrow could be almost as high as the one in January - really no changes have been made to [Theresa May's] withdrawal agreement or declaration on the future relationship.
"Some senior Conservatives... are trying to urge the Prime Minister to avoid that defeat."
However, Downing Street earlier insisted the vote tomorrow is going ahead - although the exact wording of the motion has yet to be confirmed.
Writing in the Daily Mail, meanwhile, Michael Gove - one of the key Brexiteers left in Theresa May's cabinet - called on MPs to back the deal.
He suggested: "Delaying and diluting what we have or leaving without a deal risks perpetuating the difficulties when we need to overcome divisions to meet new challenges.
"It’s time we became one nation once again."
On Friday, the EU's chief negotiator Michel Barnier publicly announced his latest proposal: a mechanism to allow the UK to unilaterally exit the customs union, but only if the backstop continues to apply to Northern Ireland.
That was swiftly rejected by the DUP and hardline pro-Brexit MPs, with the DUP's Nigel Dodds claiming the proposal was "neither realistic nor sensible."
