Britain's Brexit secretary is also meeting the EU's chief negotiator
The British Prime Minister Theresa May has questioned calls from the British Labour leader to keep the UK in a customs union with the European Union.
She has responded to a letter from Jeremy Corbyn, setting out his conditions to support a Brexit deal.
Mrs May is asking for further cross-party talks "as soon as possible".
Meanwhile, Britain's Brexit Secretary Stephen Barclay will meet the EU's chief negotiator Michel Barnier for talks in Brussels later as the deadlock continues.
Mrs May has accepted the offer of more talks with Mr Corbyn and indicated their teams should meet "as soon as possible" - with fewer than 50 days to go until the UK leaves the EU.
She vowed to take up the points raised by Mr Corbyn in a letter, replying to an earlier one sent by the Labour leader setting out his price for passing a deal.
Mrs May asked Mr Corbyn to sit down with Downing Street aides to "discuss the exact nature of those alternative arrangements".
The current backstop would see the UK remain in a customs union with the EU, with Northern Ireland retaining some extra regulatory alignment to keep an open Irish border
Mrs May gave brief responses and questions to some of Mr Corbyn's points, but said the details were best hammered out between their teams.
She added it was "good to see that we agree that the UK should leave the EU with a deal" and that it remains the most "urgent task at hand".
MPs are gathering in Westminster on Monday for another crucial week of Brexit debates as the Brexit secretary heads to Brussels for talks with the EU's chief negotiator.
Mrs May has promised MPs a chance to propose and vote on their own Brexit plans on Thursday - if she has not returned with a re-negotiated deal by then.
The EU and its leaders has ruled out changing the withdrawal agreement - but indicated it could add further clarifications about the backstop, or update the non-binding political declaration on the type of future relationship it wants to pursue with the UK.