"I don't envisage, not even for one second, Greece leaving the euro area. This is nonsense; this is propaganda," said Jean-Claude Juncker, the Luxembourg Prime Minister who chairs the Eurozone meetings of finance ministers.
"The exit of Greece out of the euro was not the subject of our debate today. Absolutely no one, absolutely no one, argued in that sense," he said after six hours of talks among the 17 ministers from the eurozone countries.
But Juncker's words also came with a warning to political parties in Greece, which have been struggling to form a government after the 6 May elections.
"The Greek public, the Greek citizens, have to know that we agreed on a programme and this programme has to be implemented," Juncker said in reference to an EU/IMF bailout package agreed last year.
EU officials have stressed that room for renegotiation of the €130 billion bailout is very small, although Juncker appeared to offer some leeway to Athens, if Greek parties manage to overcome differences and back the bailout reform plan.
"If there were to be dramatic changes in the circumstances, we wouldn't preclude a debate about an extension of the period [for Greece to meet targets]," Juncker said.
Despite the official line that Greece should stay in the eurozone, talk has been gathering pace in Brussels and other European capitals that Athens might have to leave – but only if it decided to.
"We cannot force a country to stay in the euro," German finance minister Wolfgang Schäuble said in an interview with the Welt am Sonntag newspaper.
"Of course we don't want that Greece leaves, that's crystal clear. But we would be quite a funny government if we did not prepare for all thinkable case scenarios," Schäuble said.
Only a few weeks ago there would most probably have been no reply if a journalist had asked the European Commission's chief spokeswoman what would happen if Greece decided to leave the eurozone, and whether the EU was making any contingency plans for such an event.
On Monday (14 May), spokeswoman Pia Ahrenhilde-Hansen was asked those questions and replied: "We wish Greece will remain in the euro and we hope Greece will remain in the euro ... but it must respect its commitments."
"Greece has its future in its own hands and it is really up to Greece to see what the response should be," she said.
Asked about contingencies, she did not rule them out.
"There are many, many questions arising and many questions open about Greece and most answers have to come from Greece and we have to respect the ongoing political process."
"Clearly, the future of Greece is in the eurozone. We are working on that."
Patrick Honohan, Ireland's central bank chief and European Central Bank policymaker, seemed to be ready for Greece to leave, saying at the weekend that a Greek exit would not be pleasant, but it would not be deadly either.
"Technically, it can be managed," he told reporters at a conference in Estonia. "It would be a knock to the confidence for the euro area as a whole ... It is not necessarily fatal, but it is not attractive."
Europeans may have reasons to believe they can cope with a Greek eurozone exit.
The biggest fear for the eurozone is that chaos in Greece could drag the much larger economies of Spain and Italy down and threaten the entire currency area's existence, a risk markets are beginning to price in.
"If Greece moves towards exiting the euro ... the EU would then need to enlarge its bailout funds and prepare other emergency measures," said Charles Grant, director of the Centre for European Reform think-tank in London.
"It would be a catastrophe for Greece to leave the eurozone, also with high contagion risks for the rest of the euro area," Belgian Foreign Minister Didier Reynders said on Monday.
But EU leaders seem to have been emboldened by a reinforced financial firewall to protect weak eurozone states, and by an injection of cheap money to banks from the European Central Bank.
European Commission President José Manuel Barroso admitted for the first time over the weekend that it would be better for Greece to leave the eurozone if it was unable to meet its obligations.
"Look, if a member of a club, I don't want to talk about a particular country, but if a member of a club does not respect the rules, it's better that it leaves the club, and this is true for any organisation or institution or any project," Barroso said at the weekend.
German Chancellor Angela Merkel, leader of the continent's biggest and strongest economy, said it would be better for Greece to keep the euro. She also said EU leaders should help it recover – but added that such solidarity would cease in what she called the unlikely event of Athens reneging on agreements.
But while it may have become commonplace to discuss a Greek exit (or Grexit as some economists call it), the practicalities and implications of such a decision are far more complicated and daunting than many outside observers tend to acknowledge.
It's not even clear Greece can leave the common currency. The EU's Lisbon Treaty does not make any such provision - it only considers a country leaving the European Union. And in theory a country cannot be forced out of the bloc - it has to decide of its own accord whether it wants to stay.
Article 50 of the Lisbon Treaty is the relevant piece of legislation dealing with a country that wants to leave. In essence it says that if such a decision is taken, an agreement would have to be drawn up with the other 26 member states setting out the arrangements for withdrawal. That would have to be approved by a qualified majority of EU countries and backed by the European Parliament.