An early morning meeting in Brussels between Juncker and British Prime Minister Theresa May, whose efforts to reach a deal broke down in failure earlier this week, was also a possibility, Juncker's spokesman said.
"We are making progress but not fully there yet. Talks are continuing through the night," Juncker's spokesman Margaritis Schinas said on Twitter,
Juncker spoke first with Irish Prime Minister Leo Varadkar then British premier May, the spokesman said.
"Early morning meeting possible with press point thereafter," Schinas said. "Tonight more than ever, stay tuned."
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European Council President Donald Tusk was also set to make a statement giving a "situational update" on Brexit at 0650 GMT on Friday, adding to the fevered speculation about a deal.
The EU earlier Thursday set a deadline of Sunday for May to reach a deal on divorce terms so they can be approved by member states in time for an EU leaders' summit on December 14-15.
