Speaking to French radio Europe 1 on Wednesday, Noyer said "the European Central Bank (ECB) can not indefinitely continue to take risks and support Greek banks."
Noyer called on the Greek government to reach "an agreement by Sunday," otherwise he says "the Greek economy will collapse into chaos."
However, he said if the Greek government comes up with "credible reforms", "financial aid" should be given to Greece.
For the head of France`s central bank, a `Grexit` does not mean "the end of the eurozone."
EU leaders warned the Greek government on Tuesday that a failure to reach agreement by Sunday would mean that negotiations are at an end. This means that Greek banks, which are nearly out of funds, would receive no further aid from the European Central Bank, and thus the country would be effectively forced out of the euro system.
Greece makes formal request for new bailout
Greece has made a formal request to the European Stability Mechanism for a new bailout loan, a spokesman for the European Stability Mechanism confirmed on Wednesday.
The request is the first step to arranging new financial aid for the cash-stricken country; the Eurogroup said in a statement that it would consider the request at meetings on Wednesday and Thursday.
Greece is reportedly seeking three-month bridge financing, along with a two-to-three year bailout of about €30 billion ($33.1 billion).
European Stability Mechanism is an European Union agency that provides support funds to member states in crisis.
Since 2010, the EU and the IMF have allocated around 240 billion euros ($265 billion) in bailout loans to Greece.
A 245 billion euro ($270.5 billion) bailout program under the European Financial Stability Facility ended late last month. Greece must make a 3.5 billion euro ($3.86 billion) payment to the European Central Bank on July 20. The Greek government has already made it clear that it lacks the funds to make the payment without bailout aid.
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