With the negotiations coming to a head, the central focus of the discussions on Thursday is thought to have been the issue of the Northern Ireland "backstop" meant to ensure there is no return of a "hard border" with the Republic.
Doubts over whether the fraught issue of European Union checks on goods entering Northern Ireland can be overcome remains, and that is stopping some traders from unwinding their short bets on the currency.
Labour demands that Britain retain "the exact same" perks it now has within the EU's customs union and single market - something May's so-called Chequers plan does not meet and which the EU rules out since London made a decision to leave both.
In a statement Mrs Foster, whose party props up the Government at Westminster, said the European Union plan would effectively mean imposing a trade barrier between the Northern Ireland and the rest of the UK.
Michael Russell will be there representing the Scottish Government and is expected to once again sound the alarm about the damage to Scotland's economy a hard or no-deal Brexit would do.
But Tory MP Helen Grant, a Tory vice chairwoman, told the BBC's Politics Live: "I think they're bluffing".
"Trade from Great Britain into Northern Ireland would be in danger of restriction".
Speaking to Northern Ireland journalists at her Downing Street office, May also said she expected immigration to be a significant issue in talks.
In London, British Brexit negotiator Dominic Raab cautioned not to be too optimistic and warned against a compromise that would give away too much.
However, she declined to say whether any end date could be included in the agreement, the final details of which are being decided in Brussels over the weekend.
A senior DUP MP said a Commons vote on Wednesday night that saw the party abstain on a piece of legislation for the first time since signing a pact to keep the Conservatives in power was a "warning" to the Government.
Brussels has suggested that in the event of no deal, Northern Ireland should stay in the EU customs union - something the United Kingdom has repeatedly rejected as it would create a new border between Northern Ireland and the United Kingdom across the Irish sea.
"Building optimism over a potential breakthrough in Brexit talks at next week's summit is continuing to encourage pound outperformance", said analysts at MUFG.
During the meeting work and pensions secretary Esther McVey pointedly refused to endorse the PM's Chequers plan while global development secretary Penny Mordaunt and the leader of the Commons Andrea Leadsom also made it clear they held deep concerns.
"More Important Things" On Her Mind Than Husband’s Sex Life
That one was too easy: "I don't know; you have to ask him", the First Lady replied. Asked if she loves her husband, she says, "Yes, we are fine". "Yes.