Dutch Prime Minister Mark Rutte and Austrian Chancellor Sebastian Kurz say they still think a Brexit deal can be reached even though the border between Ireland and Northern Ireland has been an impasse in negotiations.
Some traders have been unwinding short positions on sterling, seeing potential for a breakthrough at Wednesday's summit.
Rutte said on Monday night: "It is not a question of do there still need to be concessions". He added the Irish border problem is "more hard to solve than Gibraltar".
The European Council will start on Wednesday evening with a debate on Brexit with the UK Prime Minister Theresa May addressing the EU27 officials.
A summit of European Union leaders this week will decide if there is enough progress for another summit on Brexit in November, the official said.
British Prime Minister Theresa May on Monday said the disagreements between the United Kingdom and the European Union should not let their disagreements leave the two sides with a no-deal Brexit.
"So it is probably inevitable that we will end up with a "No Deal" scenario", he said.
The PM is expected to try to convince European Union leaders to drop their Irish backstop proposal at a "make-or-break" summit dinner on Wednesday night. The discussions appear to have made little headway in recent days and expectations of a deal at that summit have been scaled back.
Theresa May has issued a dramatic unity plea to ministers, calling on them to "stand together" for the sake of a Brexit deal.
May says treating Northern Ireland differently from the rest of Britain would mean, in effect, that there would have to be "a border in the Irish Sea", separating two parts of Britain.
Irish Taoiseach Leo Varadkar suggested a deal may be delayed as late as December.
He added: "But let me be absolutely clear".
The EU said it was pressing forward with contingency plans to protect the 27 remaining member states if Britain crashes out of the bloc with neither a deal in place nor a transition period established.
"We are not there yet", he said. This may not go as well as she hopes: Labour would be deeply foolish to tie themselves to a compromise deal which will be detested by Remain and Leave voters alike.
"We still have ample time to make it work", he wrote. The sticking point remains the thorny issue of the Irish border.
"Given the way in which the European Union has behaved and the corner they've put Theresa May into, there's no deal which I can see at present which will command a majority in the House of Commons", Wilson told the Belfast News Letter.
Talks among key officials in Brussels on Monday are cancelled for now.
After being destabilized and threatened to be toppled for many months by extreme Brexiteers, the British Prime Minister seems to have regained control of the party.
"There is a better solution ..."
"We are going to take this time calmly, seriously to reach this comprehensive agreement in the coming weeks". "That's new. It hasn't been there before".
Britain has proposed staying aligned to the EU's customs rules until a wider trade deal can be signed that avoids the need for any frontier checks.
He said it must be orderly for everyone, including Ireland, and a solution must be found to avoid a hard border.
This week's EU Summit will, most likely, not come up with a decision about the divorce deal.
The talks between the two men were not acrimonious, I'm told, but they got stuck - gummed up in the details of the backstop we discuss so often here. Whether we do this week or not, who knows?
The Tanaiste and Minister of State for European Affairs Helen McEntee have travelled to Luxembourg for Brexit talks at the General Affairs Council.