Greece has formally requested a loan extension from eurozone finance ministers, saying it is "optimistic" about a compromise with European Union and European Central Bank to avoid a looming exit from the union.

Athens sent a letter to Jeroen Dijsselbloem, head of the Eurogroup, to request an extension of up to six months on its European loan agreement that would sidestep the restrictions of a full-blown bailout.

"Received Greek request for six months extension," Dijsselbloem who is also the Dutch finance minister said on his Twitter account on Thursday.

Greek Finance Minister Yanis Varoufakis insisted a deal was still possible even after a firm preemptive "nein" from EU paymaster Germany to its planned offer.

"We are on the right path, I am optimistic it will end well tomorrow or the next day," Varoufakis told reporters on Wednesday.

'Grexit'

"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," he said.

Europe and Greece are racing to reach a deal to avoid a Greek exit from the eurozone - dubbed a "Grexit" - after talks in Brussels ended in acrimony on Monday with both sides digging in their heels.

The ECB decided on Wednesday to extend and increase the amount of emergency liquidity available to Greek banks to $77.5 bn, according to a bank source.

Eurozone finance ministers have given Greece until Friday to request an extension of its current austerity and reform programme.

Source: Agencies