BRUSSELS (Reuters) - The European Commission added to mounting confidence in Brussels that it is set for a Brexit deal with London when it scheduled talks with EU lawmakers ahead of a crunch meeting on Monday with Theresa May. However, EU officials and diplomats cautioned on Sunday that it was still unclear that a deal would be struck with the British prime minister when she meets the EU executive. Two hours before they sit down for lunch with May in Brussels, Commission President Jean-Claude Juncker and his Brexit negotiator Michel Barnier will brief Guy Verhofstadt and his European Parliament Brexit team, an official said. Verhofstadt and his colleagues wrote to the EU negotiators last week to sound an alarm at what they said were  stalled  talks on EU demands that the rights of EU citizens in Britain be guaranteed directly by the European Court of Justice after Britain leaves the European Union. They also voiced concern about Northern Ireland. Parliament must ratify any treaty on Britain s withdrawal from the European Union before Brexit in March 2019 in order to create the smooth transition period May wants, and so it will be vital to both sides to keep the legislators on board. Senior EU officials and diplomats said work was continuing on Sunday. One person close to the discussions said the situation was  delicate .  It s still quite fluid,  said a second person involved.  Nothing is agreed until everything is agreed.    Verhofstadt, a former Belgian prime minister and strong critic of Brexit, declined to comment. The German leader of the center-right group in the EU parliament warned that lawmakers were not yet satisfied.  On Brexit negotiations, money is one of the problems, but it is not the biggest one,  Manfred Weber said in a statement.  We are much more concerned about the fact that so far negotiations are stalled on the protection of EU citizens  rights after Brexit and on the Irish case,  he said. The EU wants outline accords on three critical divorce terms before it will open negotiations on the transition and a future free trade pact that would follow. May s lunch on Monday is a deadline for the EU to have her final offers before EU leaders consider whether to agree at a Dec. 15 summit to launch Phase 2. Britain and the EU aim to sign a joint declaration setting out progress toward final deals which the Commission, as the EU executive, would say was  sufficient  for opening trade talks. EU officials say terms have been agreed for a financial settlement long resisted by hardline supporters of Brexit. The Irish prime minister said on Saturday that would essentially cover all the 60 billion euros the EU had demanded.  On the second key issue of a deal to avoid a  hard border  on land between Britain and the EU across the island of Ireland, diplomats say the joint document will set out rules for reaching a border deal aimed at avoiding disruption to peace in the north but leaving open many of the details. The third issue, of citizens  rights, has long seemed the least problematic, but the European Parliament s concerns were a reminder of how far the insistence on the ECJ having the final say in whether London was respecting the withdrawal treaty conflicts with British demands to be free of EU courts. It was not immediately clear what compromise, if any, has been found. EU governments had also been pressing London to give better terms to EU expatriates on bringing in future family members and on moving social welfare benefits across borders. One suggestion in Brussels has been to limit clearly any ECJ involvement as a last resort and clearly only available to those EU citizens who choose to go on living in Britain before Brexit, not to any who arrive later. There are 3 million of them today. Looking to show skeptical pro-Brexit allies that she has secured something in five months of negotiation that seem set to end with London broadly accepting the EU s original terms, May has insisted that Brussels make a simultaneous and reciprocal commitment to transition and trade talks if she accepts a deal. That seems set to be the case with the joint declaration.  Everyone knows we have to honor politically what the Brits have accepted on money,  a senior EU diplomat said.  So on Monday they will sign this document.  If all goes to the plan, 27 EU leaders would give the official green light on Dec. 15, a day after May has joined them for a routine summit on other EU business.. The deliberately vague concept of  sufficient progress  gives the political leaders the option to leave plenty of room for future negotiation. The key thing for many in Brussels is that it should mark the establishment of trust that both sides are willing to work for a separation that is not too disruptive. 