It is not clear however whether the Socialists would win an absolute majority in 300-seat parliament and end up governing alone.
Under Greece's electoral laws, the winner needs 42.5 per cent of the vote for an absolute majority. If Papandreou fails another election will be needed.
Polling stations were set to open at 04:00 GMT on Sunday to allow around 9.8 million voters to cast their ballots.
The first exit polls are expected immediately after voting stations close at 1600 GMT.
Greece's conservatives won 41.8 per cent of the vote and 152 seats in parliamentary elections in September 2007.
PASOK garnered 38.1 per cent of the vote and 102 seats.
Parties expected to pass the three per cent hurdle to enter parliament, include the Communist Pary of Greece KKE, the Coalition of the Radical Left (SYRIZA) and the ultra-conservative People's Orthodox Alarm (LAOS).
Both Kramanlis and Papandreou have pledge to pull Greece out of economic crisis in the coming years and to root out corruption.