The European Commission said in a statement that it recommended to EU leaders this week "to conclude that sufficient progress" had been made to move talks along to next stage.
"We are making progress but not yet fully there", Commission spokesman Margaritis Schinas said.
Speaking on Friday morning following the news that a compromise had been made on the Irish border during the first phase of Brexit talks, Ms Foster expressed relief that an agreement had been reached regarding Northern Ireland's inclusion in a post-Brexit UK but also called for greater clarity around any future "alignment" arrangements.
Mrs May has said she wants a deep and special partnership and a better deal than the free-trade agreement that Canada secured from the EU.
'And we look forward to further clarity about what the UK's objectives are for that new relationship as well as a firm commitment on transition in the very near future'.
A spokesman for the Liberal Democrats, who are fighting for United Kingdom voters to be given a second referendum on any final Brexit deal, said: "So Theresa May has finally got a deal, but how long before it's torn apart by her own MPs?"
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While overall homelessness increased by 0.7% nationally since 2016, since 2010 there was a decline of 13.1%. Since 2010, however, veteran homelessness in IL declined by 23.7 percent and by almost 46% nationally.
The political editor of Sky News, quoting a DUP source, said the party would continue to work on the border issue on Friday.
Barnier informed European Union ambassadors that Downing Street had told him a potential solution was being worked out that could possibly satisfy both Northern Ireland's Democratic Unionist Party (DUP) and Ireland, but that it had yet to be signed off by any of those involved, the Guardian reported on Thursday.
On Thursday evening, an Irish Government spokesman said: "Matters are being considered as part of ongoing discussions involving the (EU negotiating) Task Force, the Irish Government and the British Government".
As speculation swirled about whether London, Dublin and Brussels were about to clinch a border deal, European Council President Donald Tusk's office said he would brief reporters at 0650 GMT on Friday before departing for Hungary.
And the UK Foreign Secretary and leading Cabinet Brexiteer Boris Johnson insisted any deal must stick to the spirit of the Leave campaign.
"We are going to take back control of our borders, of our laws and of United Kingdom cash contributions and that's the way forward, and we will come up with a solution", he added.