Chancellor Philip Hammond has said he is “optimistic” Brexit talks between the government and Labour can reach “some form of agreement”.
Mr Hammond said the government had “no red lines” and an “open mind”.
But Labour’s Diane Abbott says the government has made “no movement” in the talks on the political declaration, which outlines future UK-EU relations.
Three days of talks ended on Friday without agreement and Labour said no more talks were planned this weekend.
Earlier, Downing Street said it was prepared to pursue alterations to its Brexit deal and was ready to hold further talks with Labour this weekend.
Speaking ahead of an EU finance ministers’ meeting in Bucharest, Mr Hammond told reporters: “We are expecting to exchange some more text with the Labour Party today, so this is an ongoing process.”
The meetings between the government and Labour have been taking place to try to find a proposal to put to MPs which could break the Brexit deadlock in the Commons before an emergency EU summit next week.
Labour has said it wants fundamental changes to the political declaration, which sets out ambitions for the future relationship between the UK and EU after Brexit – including on trade, regulations, security and fishing rights – but does not legally commit either party.
Shadow home secretary Diane Abbott told BBC Radio 4’s Today programme that Labour had engaged in the talks “in good faith” and shadow Brexit minister Sir Keir Starmer had written to the government to say he wants them to continue.
However, she said there was concern the government did not want to alter the political declaration.
On Friday, Sir Keir said ministers were not “countenancing any change” to the “actual wording”.
“We do need change if we’re going to compromise,” he said.
Mr Hammond told reporters in Bucharest: “We should complete the process in Parliament… but we should be open to listen to suggestions that others have made.
“Some people in the Labour Party are making other suggestions to us. Of course, we have to be prepared to discuss them… in a constructive fashion.”
Earlier, a Downing Street spokesman had said “serious proposals” were made and it was “prepared to pursue changes to the political declaration in order to deliver a deal that is acceptable to both sides”.
BBC political editor Laura Kuenssberg said: “The sense is that the government has only offered clarifications on what might be possible from the existing documents, rather than adjusting any of their actual proposals in the two documents.”
She added that both sides agreed the talks are not yet over, but there were no firm commitments for when further discussions might take place.
The UK is due to leave the EU on 12 April and, as yet, no withdrawal deal has been approved by the House of Commons.
Many MPs believe leaving without a formal deal would create problems for businesses and cause difficulties at ports.
Prime Minister Theresa May has written to European Council President Donald Tusk to request an extension to the Brexit process until 30 June.
A senior EU source told BBC Europe editor Katya Adler that Mr Tusk would propose a 12-month “flexible” extension, with the option of the UK leaving sooner once Parliament had ratified a deal.
Any extension would have to be unanimously approved by EU leaders.
Irish Prime Minister Leo Varadkar said a longer delay to Brexit “might make more sense” than the UK seeking “an extension every couple of weeks or every couple of months, because that just adds to the uncertainty for citizens, for businesses and for farmers”.
However, French Europe minister Amelie de Montchalin said such a delay would require the UK to put forward a proposal with “clear and credible political backing”.
“In the absence of such a plan, we would have to acknowledge that the UK chose to leave the EU in a disorderly manner,” she added.
Mrs May says that if the Commons agrees a deal in time, the UK should be able to leave before European parliamentary elections are held on 23 May.
But the UK would prepare to field candidates in case MPs failed to back a deal, she said.
The prospect has angered many Conservatives, with prominent Brexiteer Jacob Rees-Mogg arguing: “If a long extension leaves us stuck in the EU we should be as difficult as possible.”