"I want to believe that we will be able to find a deal with our British friends between the European Council meeting next week and the possible one in November," Juncker told French newspaper Le Monde.
"We therefore need substantial progress, which we should be able to see next week," Juncker added, referring to a meeting of EU leaders in Brussels where Britain's exit from the European Union is set to top the agenda.
If she cannot convince them that she is able to deliver a Brexit deal that her European counterparts see as respecting the EU's joint rules on trade and investment, negotiations are expected to fall into crisis.
The biggest difficulty is the future trading and customs arrangement between Ireland, an EU member, and northern Ireland, a British territory that will leave the trading bloc in March next year along with the rest of the UK.
"The Irish question is obviously ultra difficult," Juncker said. "It's true that we are not where we need to be to be able to conclude. (But) it's not the EU that has imposed this debate on the British and Irish: it's the sovereign British decision that caused this difficulty.
Juncker said that the EU Commission and member states were preparing for a potential "no deal" scenario that would see Britain crash out of the EU next March without legal agreements governing its relations with the rest of the bloc.
"Some (members) consider that we should do more (to prepare for a no deal"," Juncker said. "I have good reasons for not doing that: we are not insisting too much because it would be seen as a provocation in London.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)