It is not clear what concessions have been offered by either side, but Greek premier Alexis Tsipras detailed what his office called a "mutually beneficial deal" in a phone call with German Chancellor Angela Merkel, French President Francois Hollande and European Commission President Jean-Claude Juncker.
Juncker's cabinet head Martin Selmayr said the Athens proposal offered "a good basis for progress", though he described the negotiations as a "forceps delivery", underscoring the exertions to prevent Greece crashing out of the eurozone.
Greece said its new proposals were aimed at reaching a "definitive solution" to end the standoff between Athens and its creditors.
Athens announced a frenzied round of meetings before the summit, with Tsipras also scheduled to meet the leaders of its International Monetary Fund, European Union and European Central Bank creditors today.
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Separately, the ECB's governing council will also meet on Monday to discuss whether to raise the level of emergency funding to Greek banks yet again, after the country's banking system came under intense pressure with clients withdrawing massive sums in savings.
Italian Prime Minister Matteo Renzi urged the two sides to seize a "window of opportunity", saying all conditions were in place for them to reach a "win-win accord".
Asian markets mostly reacted positively in morning trade, with Tokyo piling on 0.80 per cent and Hong Kong up 0.44 per cent by the break.
The euro also ticked higher, buying USD 1.1381 and 139.70 yen in Tokyo compared with USD 1.1349 and 139.23 yen in New York late Friday.