During the weekend, Stournaras said "significant progress on many levels" had been made.
Greece's progress in meeting the terms of its $170 billion international bailout will be reviewed at the end of the week when finance ministers from Europe meet in Dublin, The New York Times reported Monday.
Greek finance leaders have been meeting with representatives of the so-called troika that oversees the bailout: the International Monetary Fund, the European Central Bank and the European Commission.
Greek and troika officials have come close to an agreement on how Greeks will be permitted to pay off outstanding tax and social security payments owed to the government. The troika is also considering a proposal to reduce the impact of a property tax that was part of Greece's austerity budgeting, the Times said.
On Sunday, Prime Minister Antonis Samaras told troika representatives Greeks had reached the limit on spending cuts and tax increases put in place to secure the international loan.