* PM May said on Friday Britain wants close EU friendship
* Brussels sees two key concessions, but wants details
* Negotiators Davis and Barnier due to meet on Monday
* Differences remain on Brexit cash, EU citizens' rights
* May meets EU's Tusk on Tuesday, EU leaders on Thursday
By Alastair Macdonald
BRUSSELS, Sept 24 (Reuters) - In pledging to stay best friends with the European Union after Brexit, Theresa May is getting ahead of herself, say EU negotiators who want her to start putting the divorce money on the table as soon as Monday.
Three days after the prime minister's speech in Renaissance Florence promising a warm and vibrant future relationship, her Brexit minister David Davis will launch a new round of talks in Brussels with the EU's Michel Barnier. And the Frenchman first wants details on May's broad promise to pay Britain's bills.
Without "significant progress" on that and other elements of a planned treaty to ease Britain's passage out of the Union in March 2019, Barnier said, EU leaders will refuse to open any talks on a free trade and cooperation deal, let alone on the two-year transition to it that May requested.
With German Chancellor Angela Merkel concentrating on her likely re-election in voting on Sunday, her coalition deputy still found time to echo French President Emmanuel Macron in ramming home the demand that Britain focus first on its exit.
"We heard nothing concrete. It is time for the government of Great Britain to clearly state under what conditions it wants to leave the European Union," Foreign Minister Sigmar Gabriel said.
May's speech was intended to jolt the divorce talks out of deadlock, three months after they began and to demonstrate some unity in her government -- notably on remaining in the EU single market and accepting its rules for a couple of years after Brexit, a bitter pill for some hardline opponents of EU membership.
But much of her 35-minute address dwelt on the "Shared Future". A Facebook video targeted at continental neighbours emphasised the message with clips from the speech. A Dutch-language version led off with the bold caption: "Wij willen uw beste vriend en partner zijn" -- We want to be your best friend and partner.
The tone went down well with some: "There are many positive elements, especially regarding the future relations," a senior EU government official said. "On the other hand, on issues related with the separation there is not much clarity. We are looking forward to receiving detailed proposals."
CONCESSIONS
May made two potentially important concessions on the other two criteria for moving on to trade talks: a direct role for the EU-UK exit treaty and for EU case law in British judges' rulings on the future rights of EU citizens in Britain; and she said Brexit would not immediately cost other states money.