Brexit: Theresa May urges new dynamic in Brexit talks
But they may agree to begin talking among themselves about trade.
Mrs May, excluded from Friday's meeting, told leaders on Thursday that "firm progress" was being made.
A source told the BBC the prime minister told them there was an increasing feeling "that we must work together to get to an outcome that we can stand behind and defend to our people".
EU leaders have gathered in Brussels for a crunch summit to assess the progress made so far in Brexit negotiations with the UK, which is due to leave the EU in March 2019, following last year's referendum result.
While Mrs May attended on Thursday, she will leave early on Friday, when the other leaders discuss Brexit without her.
They are expected to officially conclude "insufficient progress" has been made in negotiations over citizens' rights, the UK's financial obligation and the border in Northern Ireland to allow them to move onto the second phase of talks dealing with trade discussions.
On Thursday, German Chancellor Angela Merkel said there were "encouraging" signs of progress in Brexit negotiations and suggested trade talks could begin in December - when EU leaders are next scheduled to meet.
She said the process was progressing "step by step" despite British media reports that negotiations were not advancing.
"I have absolutely no doubt that if we are all focused - and the speech in Florence made a contribution towards that - we can achieve a good result," she said.
"From my side there are no indications at all that we won't succeed."
Over a working dinner of gnocchi and "pheasant supreme" on Thursday night, the prime minister told fellow EU leaders she was determined the UK would be a strong partner on issues from security, defence and climate change to trade, a senior government source told the BBC's Laura Kuenssberg.
The PM told them the EU-UK's future relationship should be a "close economic partnership" which supports "prosperity for all our peoples" and that they could be optimistic and ambitious as they already shared "the same set of fundamental beliefs".