The Brexit crisis threatens to overshadow the meeting in the Swedish port city of Gothenburg, which is supposed to focus on fair jobs and growth in the European Union.
May will hold talks with EU President Donald Tusk as a deadline looms for Britain to make enough progress to move on to trade talks in December.
“Tusk will inform May that such a positive scenario is not a given, will require more work and that time is short,” an EU source told AFP of the meeting at 12.30pm.
Former Polish premier Tusk “will ask May how the UK plans to progress” on key issues before negotiations can advance to the next phase, which includes post-Brexit trade ties and a transition period.
She met Swedish Prime Minister Stefan Löfven, who is co-organizing the summit, on Thursday.
“Sweden and Britain have a good relationship and we want to keep that after Brexit,” said Löfven.
The EU demands that Britain makes sufficient progress on its exit bill, on avoiding a hard border between the British province of Northern Ireland and the EU state of Ireland, and on the rights of three million EU citizens living in Britain.
EU Brexit negotiator Michel Barnier warned last week that Britain and two weeks to meet the bloc's conditions if it wanted an agreement at the next EU summit in Brussels in December.
Failure to do so would push back a decision until February or March, leaving little time for trade talks before Britain leaves the bloc in March 2019.
'All about people'
The so-called “social summit” in Sweden is the first step in a two-year reform drive to show the bloc can survive after Brexit and other setbacks by tackling the economic inequalities fuelling populism.
EU leaders are looking to reboot the union based on plans by France's dynamic new president Emmanuel Macron and European Commission head Jean-Claude Juncker.
By holding their first “social summit” since one in Luxembourg in 1997, they aim to show the post-war dream of a united Europe is still alive by promoting fair jobs, growth and a social safety net after years of economic austerity.
An EU source told reporters in Gothenburg that despite Brexit, May herself fully supports the social reform agenda embraced by EU leaders in Sweden.
Swedish Prime Minister Löfven said far-right gains in Austrian and German elections this year, which followed last year's shock of Britain's vote to leave the European Union, showed action was necessary.
“I'm convinced that a sustainable European Union needs a strong social dimension because this is all about people,” Löfven told AFP in an interview in Brussels last month.
Most of the EU's 28 national leaders are attending the talks, including France's Emmanuel Macron.
But Chancellor Angela Merkel of Germany, the bloc's economic and political lodestar, will skip the summit to lead talks for a new governing coalition, though her aides said she fully supports the meeting's goals.
These points will be enshrined in a European Pillar of Social Rights which Juncker, European Parliament chief Antonio Tajani and Estonian Prime Minister Juri Ratas – whose country holds the EU's rotating presidency – are due to sign on Friday.