BRUSSELS (Reuters) - European Union negotiators see no big breakthrough in a new round of Brexit talks from Monday nor when Theresa May attends a summit next week, yet leaders could offer the beleaguered British prime minister a hand, EU officials believe. Talks which began on Monday in Brussels have a thin schedule - British Brexit Secretary David Davis is to meet EU negotiator Michel Barnier on Tuesday and again on Thursday. But Wednesday is blank on the timetable and officials will not touch on the knottiest outstanding problem - how much Britain pays the EU.  That all but rules out  miracles  on key divorce issues that Barnier s boss says are needed for May s 27 fellow EU leaders to agree to open the talks she wants on a post-Brexit free trade pact when they all meet in Brussels next Thursday and Friday. The prime minister revived an increasingly sour dialogue two weeks ago by offering concessions in a speech in Florence. But talks that followed left big gaps on three core issues on which the EU demands  significant progress  before Barnier can so much as mention what happens after Britain leaves in 18 months time. Yet such is the opposition to compromise that May faces within her own party that many EU diplomats think leaders could give her some hope at the summit to help her face down calls for Britain to simply walk out without a deal - an eventuality that the Europeans are nonetheless preparing for.  My guess is the leaders will try to find some positive elements,  one senior diplomat told Reuters, saying May could be offered hope of a  landing zone  for accords to let the next scheduled summit, in mid-December, approve trade talks. This week could see further movement on agreeing rights for expatriate citizens, where the role of EU judges is in dispute.    But few see much movement on the Irish border or on the money. And with May and the EU batting back and forth assertions that the ball is in the other s court, attention is fast turning from this week s meetings to next week s summit.  Not one of over a dozen senior EU officials and diplomats who spoke to Reuters expect the summit to launch talks on future trade, few rule out that May s counterparts may give her some assurance of doing so soon - and even offer some limited exploration of the transition period she has asked for.  She is in a difficult situation, if she goes out there and there is nothing tangible on our side,  a senior EU official said, saying governments wanted to keep up momentum for a deal that would avoid legal chaos across Europe.  We ll try to be neutral, maybe even offer an encouraging line to stay engaged.  Nonetheless, governments are extremely wary of any attempt by British negotiators to divide their solid display of unity and are anxious not to appear to be going soft on May, despite some sympathy for the balancing act she faces. On Friday, envoys from many of the 27 including heavyweights Germany and France opposed suggestions from Barnier that they might start some preliminary discussion of what exactly will happen in the transition period immediately after Brexit.  This situation is not a reason for the Commission to loosen its guidelines,  a senior official from a big EU power said of May s domestic woes.  I believe she really wants a deal but we can t alter our negotiating stance because of that.  Nonetheless, several diplomats said leaders could soften the stance on transition talks by next week. Leaders say they will not negotiate directly with May and want to channel everything through Barnier. But May s powerful peers may find it hard to sit back and watch her fail, provoking further British turmoil.  The leaders want to lead, they want to make history,  said another senior EU diplomat who said the summiteers could break next week from the advice of their own officials.  Who can say that they won t just say,  OK, let s just get on with it ?  