BRUSSELS/LONDON (Reuters) - Britain has offered to pay much of what the European Union was demanding to settle a Brexit  divorce bill , bringing the two sides close to agreement on a key obstacle to opening talks on a future free trade pact, EU sources said on Tuesday. The offer, which British newspapers valued at around 50 billion euros (44.3 billion pounds), reflected the bulk of outstanding EU demands that include London paying a share of post-Brexit EU spending on commitments made before Britain leaves in March 2019 as well as funding of EU staff pensions for decades to come. A British government official said they  do not recognise  this account of the talks going on ahead of a visit by Prime Minister Theresa May to Brussels this coming Monday. EU officials close to the negotiations stressed that work was still continuing ahead of May s talks with European Commission President Jean-Claude Juncker and his chief Brexit negotiator Michel Barnier. But EU diplomats briefed on progress said the British offer was promising and that, on the financial settlement, the two sides were, as one said,  close to a deal . Nonetheless, others cautioned that Britain had yet to make a fully committed offer and that essential agreement from the other 27 member states could not yet be taken for granted. The EU set the condition of  significant progress  on three key elements of a withdrawal treaty before it would accede to London s request for negotiations on a free trade pact that could keep business flowing after Brexit in 16 months. It set a deadline of Monday for that progress to be made if EU leaders were to give a green light at a summit on Dec. 14-15. On the issue of the rights of EU citizens in Britain, EU negotiators are still pressing Britain to accept that European judges should have a final say on enforcing those rights. If the financial settlement, which many British businesses have argued May should make in order to avoid a disruptive  cliff edge  departure from the single market, is forthcoming, the thorniest outstanding issue is that of the Irish border.  Ireland remains the most difficult issue,  a senior EU diplomat said after Irish Prime Minister Leo Varadkar avoided a disruptive snap election when his deputy resigned on Tuesday at the insistence of the party propping up his minority government. Britain has yet to satisfy EU - including Irish - demands that it clarify how it would avoid a  hard border  with customs posts on land between Northern Ireland and the EU. Many fear that would disturb the fragile peace in the British province.  On the Brexit bill, Juncker has estimated Britain would owe roughly 60 billion euros. EU officials say Brussels is willing to work with May to massage those figures in order to help her win backing from hardline Brexit supporters who have in the past insisted that Britain owes Brussels nothing. Britain s Financial Times said London agreed to assume liabilities worth up to 100 billion euros, but said net payments over many decades could fall to less than half that amount. The European Commission declined to comment. Britain s Brexit ministry said  intensive talks  were continuing and the two sides were trying to find a way to  build on recent momentum in the talks  to take them to the next stage. Sterling rallied around 1 percent against the U.S. dollar as investors took the reports as a sign that the risk of Britain leaving the EU without a deal, which is widely seen as damaging to the economy, had diminished. 