* EU sources say Britain giving ground to secure transition deal
* May "confident" of agreement at next week EU summit
* Diplomats warn Irish border issue risks derailing deal
BRUSSELS, March 15 (Reuters) - Prime Minister Theresa May and British businesses are banking on European Union leaders granting a Brexit transition deal next week but diplomats said they could face disappointment unless a deadlock is broken over the Irish border.
May's spokesman said on Thursday she remained "confident" of a deal that would reassure investors that little will change in trading with the bloc for around two years after Britain leaves next March and until a new trade pact can be agreed.
EU diplomats and officials said talks have raised their hopes too that, with London anxious for a quick deal, the bloc's leaders can endorse a transition at a Brussels summit on Friday.
But what some described as complete stalemate on Irish border arrangements risks derailing any agreement.
"This whole thing could end in tears," one senior diplomat said. "British business might get a terrible shock."
Asked about those concerns, a British government source conceded that there was still "a lot left to do".
The EU is irritated by Britain's refusal to accept in the draft withdrawal treaty the inclusion of a "backstop" solution to avoid a disruptive hard land border between EU member state Ireland and the British province of Northern Ireland.
Sterling has suffered before when Brussels has warned that a transition deal cannot be taken for granted. It will not become certain until the whole withdrawal treaty is ratified, probably early next year, but Britain hopes for an interim EU commitment.
"No one will promise May a transition just like that," a second diplomat said after envoys from the 27 remaining states discussed EU negotiators' latest draft (http://bit.ly/2FCnGZ8).
"But there is something in the air, there is optimism. Cautious, but optimism. We want to use the fact that Britain wants the transition so much, we would hope many things will therefore move. We will stress the Irish issue."
Another EU diplomat echoed that view, saying: "There is a lot of movement. All the rest can be sorted out. But unless Ireland is sorted out, there is no transition deal at the summit."
Germany's Brexit coordinator said "a lot of progress" was being made. Some foresaw a possible "fudge" of the Irish issue, as happened to secure a first interim accord last December.
Dublin insists London must accept the "backstop" which the EU says May agreed to as part of the interim deal in December.
That would see the province effectively retained inside an EU-run customs area, isolated as result from the British mainland.
May, who relies on Northern Irish votes in parliament, has rejected that and said better solutions will have to wait for separate talks on future UK-EU trade, due to start this spring.
There has been progress this week in narrowing differences on such issues as expatriate citizens' rights, copyright and nuclear cooperation. But EU negotiators are reluctant to give away leverage they believe they need to cut a final deal.
"We won't just offer transition like that next week," a fourth EU diplomat said. "We would lose a lot of leverage, risk Ireland. But the latest talks have covered ground. So we'd look for a wording to recognise that and lock that progress.
"To send a positive signal ahead. They will get it -- if they accept our conditions," the diplomat added.
Negotiations are set for over the weekend and senior British representatives will be in Brussels on Monday and Tuesday.
May will attend the summit on Thursday, although Brexit will not be formally discussed. She may seek support against Russia over the nerve agent attack on a Russian former spy in Britain.
Any Brexit transition deal will be discussed by the other 27 leaders when they reconvene without May the following day.
(Additional reporting by Jan Strupczewski and Alastair Macdonald in Brussels and Elizabeth Piper in London, Editing by Alastair Macdonald and Catherine Evans)