"So far no white smoke. We stand ready to receive prime minister May at any moment in time when they are ready," Margaritis Schinas, chief spokesman for commission chief Jean- Claude Juncker, told reporters in Brussels.
The Vatican sends up white smoke when a new pope is chosen.
"But I would like to repeat what President Juncker said on this, namely that this will have to happen this week, in this building. We work for a full week, 24/7, and our week includes Sunday."
Time is now running out for a deal on Brexit divorce terms, which would allow the opening of talks on a future trade deal at a summit of EU leaders in Brussels on December 14-15.
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Schinas dismissed British newspaper reports that the deadline could be extended into next week as "not correct".
Diplomats from the other EU 27 nations are to meet on Monday and would need to see European Council chief Donald Tusk's draft guidelines for opening the next phase of talks then in order to approve them for the summit, he said.
"Every day lost makes this more difficult," he said. "President Juncker is a born optimist... but it takes two to tango, two to be optimist."
But EU sources said it was still possible that European leaders could agree at the summit next week that there had been "sufficient progress", in order to give May a win, while postponing their approval of the guidelines for trade talks.