Juncker said in an interview last week, broadcast on Sunday (September 22), that he is doing everything to secure a deal, because of the "catastrophic consequences" of a no-deal.
He also reiterated that if Britain left the European Union without a deal there would be a new border between Northern Ireland and Ireland.
In a Sky News interview, he said: "Yes ... We have to make sure that the interests of the European Union and of the internal market will be preserved."
Three years after Britons voted to leave the EU, hopes of a breakthrough over the terms of its departure have been stoked in recent days by British Prime Minister Boris Johnson saying the shape of a deal is emerging and Juncker saying agreement is possible.
But diplomats say the two sides are split over London's desire to remove the Irish border "backstop" from the divorce deal struck by Johnson's predecessor, Theresa May, and then work out a replacement in coming years.