Eurogroup chief Jeroen Dijsselbloem said on his Twitter account that he had received the request, without giving further details.
"Received Greek request for six months extension," said Dijsselbloem, who is also the Dutch finance minister.
Athens is trying to sidestep the restrictions of its bailout, but a number of eurozone hardliners including Germany are likely to resist the move.
"Our proposition will be written in such a way that it will cover both the demands of the Greek side and the head of the Eurogroup," Greek Finance Minister Yanis Varoufakis told reporters late yesterday.
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The European phase of Greece's EU-IMF bailout expires on February 28, and Athens needs to find 11.9 billion euros (USD 13.5 billion) for bond repayments to the IMF and the European Central Bank by August.
Athens is under mounting pressure to reach a deal to forestall a bank liquidity shortage and lasting damage to its fragile economic recovery.
The European Central Bank decided yesterday to extend and increase the amount of emergency liquidity available to Greek banks to 68.3 billion euros (USD 77.5 billion), according to a bank source.
The new radical government of Prime Minister Alexis Tsipras that came to power last month wants to reverse many of the fiscal reform obligations tied to the EU-IMF rescue packages which have been keeping the country afloat since 2010.
The government has halted privatisations and promised to increase wages and roll back labour market reforms.