Juncker's words in an interview with Sky News are seen to strike a more accommodating tone, though European Union figures have made the same point in less stark terms before and the gap between both sides remains significant.
"We were getting into the detail".
But the commission cautioned that "it is essential that there is a fully workable and legally operational solution" included in the legally binding Brexit divorce agreement.
The British prime minister Boris Johnson told reporters that some "progress" was being made in talks with Brussels, yet cautioned it was important not to "exaggerate" this.
In the interview with Sky News, Juncker said: "I had a meeting with Boris Johnson that was rather positive".
After months of stalemate, the two sides have begun to sound slightly more optimistic.
Mr Coveney said: "There are serious problems that arise because of the change in approach by the British Prime Minister - asking to remove a very significant section within the Withdrawal Agreement without any serious proposals as to how you solve those problems is not going to be the basis for an agreement".
"But I think we need to be honest with people and say that we're not close to that deal right now".
But the Government insisted Mr Johnson will not be bound by an "artificial deadline" to produce formal written proposals.
Britain says it has not revealed detailed proposals because they would likely leak, to the detriment of negotiations.
The European commission team was told by Whitehall that the three "confidential" papers it had sent on Thursday evening should not be distributed to Brexit delegates representing the EU's 27 other member states. One of the UK's paper opens discussions on its scope.
It says the European Union remains "willing and open to examine any such proposals that meet all the objectives of the backstop" proposal now in the agreement but which Britain wants removed.
Sterling has fallen in recent months as fears have grown of a damaging no-deal Brexit, but it rallied last week as the United Kingdom government talked up new proposals and Juncker's comments late on Thursday gave investors fresh hope.
London proposed to Brussels earlier this month that common rules for checking animals and animal products could be established across the island of Ireland as part of an alternative to the backstop arrangement.
Mulhall said, "There are those who think that maybe a solution could be to have a backstop for Northern Ireland only, but that's something that doesn't seem to be popular with the British government".