Christine Lagarde Yanis Varoufakis
Greek Finance Minister Yanis Varoufakis talks to International Monetary Fund managing director Christine LagardeReuters

International Monetary Fund chief Christine Lagarde has refused to rule out a possible Greek exit – or Grexit – from the eurozone.

Lagarde told German newspaper Frankfurter Allgemeine Zeitung that she could not "preclude" a Greek exit, after four months of tortuous bail-out talks that have failed to get both sides closer to a deal to release aid to the country.

"No one wishes the Europeans a Grexit," she said in an interview on 28 May.

And despite reports that progress had been made with cash-strapped Athens over a bailout Lagarde said recent optimism over the country's future had "sobered".

"It's very unlikely that we will reach a comprehensive solution in the next few days", she told the daily during a summit of G7 leaders in Dresden.

It would not be "a walk in the park" for the single currency, but would "probably not be an end to the euro", Lagarde added.

Athens has warned it will be unable to repay a €300m (£215m, $330m) loan to the IMF on 5 June, without more help aid from its creditors. Both the IMF and European Central Bank have ruled out giving Athens any of the €7.2bn tranche of emergency cash it requires without a very reluctant Greek government coming up with reforms for a "comprehensive" deal being struck between the parties.

Lagarde has already warned there would be no "quick and dirty" deal.

"We have rules, we have principles. There can be no half-baked programme review," said Lagarde.

Without an agreement, the eurozone would be left holding Greece's debt baby, which the bloc's largest creditor, Germany, would rule out.