"The European Council expresses its concern that no substantial progress has yet been achieved on agreeing a backstop solution for Ireland/Northern Ireland", the draft conclusions, seen by Reuters, said.
Juncker's a two-day visit to Dublin, accompanied by EU Brexit negotiator Michel Barnier and EU Agriculture Commissioner Phil Hogan, is meant to reinforce the message that the rest of the EU will continue to stand shoulder to shoulder with Dublin on the border issue.
And to be a backstop "it needs to actually solve the problem; so it needs to do with customs and regulatory issues, and it needs not to have an expiry date".
Coming a week ahead of a key European Council meeting of leaders in Brussels, the visit to Dublin of Mr Juncker and the EU's chief Brexit negotiator Michel Barnier is a clear demonstration of the EU's solidarity with Ireland's position.
"We have been reassured over and over again that Ireland will not be left isolated here", he said.
The marine environment is listed as the main topic for discussion, but Brexit is expected to be debated ahead of next week's European Union summit in Brussels.
"Ireland has to be part of the deal", he added.
"I am strongly against any temptation to isolate Ireland and not to conclude the deal on Ireland".
According to The Telegraph, he added: "It is a real honour to be with you here today for this special sitting of the joint houses".
Ireland's prime minister warned Britain on Thursday that there is not much time left to conclude a smooth withdrawal from the European Union, as the head of the EU's executive arm pledged its full support for Dublin's stance.
The majority of Brexit voters would still choose to leave the European Union even if it caused the United Kingdom to split, the latest Lord Ashcroft poll claims.
"There has been consistent recognition of the unique position of Northern Ireland, and the unique situation in which it has been put by the decision of the United Kingdom to leave the EU".
Mr Junker will receive an honorary doctorate from the National University of Ireland and attend an official dinner hosted by Mr Varadkar in Dublin Castle later on Thursday.
Across Great Britain, 62 per cent of respondents said Brexit negotiations were proceeding too slowly, with 30 per cent blaming the delays on "politicians in Britain who want a soft Brexit or to stop Brexit altogether".
The future of the border between European Union member Ireland and Northern Ireland after Brexit is one of the most hotly contested issues in the negotiations, with many on both sides of the border wanting to keep the current free-flowing frontier open.
But there will be no withdrawal agreement without a fully operation backstop.