According to the Pulse and MARC polls, New Democracy and the next-biggest pro-bailout party, the socialist PASOK, would together win a parliamentary majority of between 11 and 16 seats in the country's 300-seat parliament.
Europe's Stoxx 600 Index edged nearly 0.1 per cent lower for the day. In London, the FTSE 100 rose 0.09 per cent; Germany's DAX slid 0.26 per cent and the CAC 40 dipped 0.16 per cent.
S&P 500 futures expiring in June were up 0.5 per cent and Dow futures advanced 0.3 per cent. Wall Street was closed for the Memorial Day holiday.
There were also holidays in Europe, closing markets in Denmark, Iceland, Luxembourg, Austria, Norway and Switzerland.
Even with a bright spot towards developments in Greece, there's plenty of concern about another euro zone member: Spain. Spain's IBEX 35 shed 2.2 per cent as bond yields climbed amid concern the country is the next one headed for an international financial bailout.
The yield on Spain's 10-year bond rose 16 basis points to 6.47 per cent. The premium investors demand to hold the securities instead of their German counterparts widened to as much as 514 basis points, the biggest spread since the euro's introduction.
Still, Spain remains adamant such a rescue won't be needed.
"There are major doubts over the euro zone and that makes the risk premium for some countries very high. That's why it would be a very good idea to deliver a clear message there's no going back for the euro," Prime Minister Mariano Rajoy told a news conference, Reuters reported. "There will not be any [European] rescue for the Spanish banking system."
Many investors aren't so sure, given the recent examples set by Ireland, Portugal and Greece, and the lingering turmoil.