When Theresa May triggered Article 50 in March this year, she kicked off what should be a two-year process. Within that timeframe, the UK is supposed to negotiate the terms of its exit, and officially leave the EU by April 2019.
However, with the EU and Britain currently in stalemate, and both parties unable to find "a real compromise as far as the remaining financial commitments of the UK are concerned", Juncker said, the original deadline now seems out of reach.
"The British are discovering, as we are, day after day new problems. That's the reason why this process will take longer than initially thought," he said.
Juncker made the comments in a speech on the future of Europe, delivered at the University of Luxembourg.
The Luxembourgish politician also said the UK will have to pay if they want to move on to the second stage of Brexit negotiations.
"They have to pay, they have to pay, not in an impossible way. I'm not in a revenge mood. I'm not hating the British," he added.
Yesterday, Michel Barnier, the EU's chief negotiator, said he would not recommend that Brexit talks move on to the second phase because the UK and the European bloc remain in a "disturbing" state of deadlock.
Speaking at the end of the fifth round of talks, Barnier said it was "within our grasp within the next two months" but not in time for the next meeting of the European Council next week.
Talks were held "in a constructive spirit", he said, but "without any great steps forward". Still, "decisive" progress could be made in time for the next European Council meeting before Christmas, he said.