The European Commission president said he was "doing everything" to get a deal as he felt a hard Brexit would be "catastrophic" for both sides.
"It's better for Britain and for the European Union to have an organised deal," he said, in an interview with Sky.
He also suggested an openness to the contentious Irish backstop plans being scrapped, so long as they were replaced with a viable alternative.
He said: "I don't have an erotic relation to the backstop.
"If the results are there, I don't care about the instrument.
"If the objectives are met, all of them, then we don't need the backstop."
The PM has frequently called for the backstop, an aspect of Theresa May's withdrawal agreement, to be abolished.
However, the EU has insisted such a measure is necessary unless a viable option to replace it is proposed.
Leaders have suggested that thus far no such new plan has been forthcoming.
Mr Juncker's comments after the PM said on Thursday: "I don't want to exaggerate the progress that we are making, but we are making progress."
But despite expressing his belief a deal could be struck, Mr Johnson said he felt there must still be preparations for no-deal and stood by his stance he would be ready for such a situation.
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The quotes from Mr Juncker come after criticism for the PM on his work on a deal from other leaders.
Michel Barnier, the EU chief Brexit negotiator, said he should "stop pretending" to negotiate.
Meanwhile the Government was set a deadline of the end of the month to give alternative proposals by Finland's PM after he met with French president Emmanuel Macron.
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