* May, Davis to dine with Juncker, Barnier at 1630 GMT Monday
* Meeting long planned before summit, London says
* Talks did not feature in Juncker, Barnier schedules
* EU leaders to meet May on Thursday in Brussels (Adds details from May's office, Juncker comment)
LONDON/BRUSSELS, Oct 16 (Reuters) - British Prime Minister Theresa May travels to Brussels on Monday for dinner with European Commission chief Jean-Claude Juncker after deadlock in Brexit talks appeared to dash her hopes a summit this week could launch negotiations on future trade ties.
May's office said the 1630 GMT meeting had been planned for weeks. However, a dinner was not on Juncker's agenda published on Friday, and EU officials said it had also not been on the schedule for the bloc's Brexit negotiator Michel Barnier, who will be at the dinner along with his British counterpart, David Davis.
After talks with Davis last week, Barnier said negotiations were deadlocked, notably over London's refusal to detail what it was offering to pay Brussels. This followed an attempt by May last month to revive the negotiations with a speech in Florence promising Britain would honour its EU commitments.
As a result, Barnier told European Union leaders not to launch the talks on a future relationship that May has demanded. As time ticks down to withdrawal in March 2019, concern is rising across Europe that the process may collapse.
"This is about reflecting upon Florence and the constructive way it's been received and that we want to continue to move forward in a constructive manner," May's spokesman said.
British Foreign Secretary Boris Johnson also urged progress in the talks: "Let's get these negotiations going and stop letting the grass grow under our feet."
But EU leaders say May has been too vague in her offer of a financial settlement -- something many diplomats believe is due to a fear that to agree even a very rough a figure would spark a backlash from hardline Brexit supporters such as Johnson.
British officials say they cannot give a figure on the final bill until they know what kind of trade agreement will be sealed during the talks.
Asked if May would flesh out details of what Britain is prepared to offer in terms of a financial settlement, her spokesman said: "The PM set out her position in the Florence speech in relation to the settlement, and that's where we are."
In response to suggestions from Barnier, EU governments have agreed, however, that the summit on Thursday and Friday should give him a green light to explore a possible post-Brexit transition period - although only in internal discussions within the EU, not with the British negotiators themselves.
Even that has run into resistance, notably from heavyweights Germany and France. They insist further progress in the British divorce package is required for any such gesture to be made to May, who is struggling to unite her own government behind her plan to reach a deal on a two-year transition during which Britain could stay in the single market and customs union.
A statement by the 27 other EU states, planned for Friday when their leaders will meet after May has left, is being redrafted to harden the conditions under which Barnier will be allowed to explore the options for the transition.
Aside from the money, where Juncker has said Britain may owe something like 60 billion euros ($70 billion), the EU says there has not been "sufficient progress" on two other critical divorce issues -- the rights of expatriate citizens and how to avoid a new EU-UK border disrupting a fragile peace in Northern Ireland.
Without meeting those three tests, the Union says there can be no opening of talks on what happens after March 29, 2019. The leaders have been expected to say they hope that they can launch that second phase of talks after their next summit in December.
With time running short, and hardline pro-Brexit ministers urging May to be prepared to walk out without reaching a deal to limit the legal uncertainties of withdrawal, continental governments have stepped up planning for a collapse in talks.
Business leaders on both sides of the English Channel have said that without clarity by the new year, they will increasingly have to take investment decisions to reflect uncertainty over British access to EU markets.
On Friday, May's spokeswoman said there would be "more to say" on Britain's financial offer at the summit on Thursday.
The dinner will involve only May, Juncker, Davis, Barnier and one other official from either side. After a similar meeting at 10 Downing Street in late April, leaked accounts of Juncker's "shock" at what he said were unrealistic British expectations irritated May.
Asked about his expectations for Monday's meeting, Juncker told reporters: "I am meeting with Mrs. May tonight. We will talk, and you will see the autopsy." (Additional reporting by Robin Emmott in Luxembourg; Writing by Alastair Macdonald; Editing by Jeremy Gaunt)