The ministers have been discussing a proposal from Greek finance minister Yanis Varoufakis since 2pm.
Varoufakis wrote to his colleagues that the reform package would "strengthen fiscal sustainability, guarantee financial sustainability and promote economic recovery".
It includes steps to tighten up tax collection and government spending, especially on the civil service and pensions, and crack down on corruption, as well as continuing moves to privatize parts of the Greek economy.
But in a bid to relieve the pain of harsh austerity measures – the promise which carried Syriza to power – the Greeks also hope ot offer free electricity for 300,000 poor families, free access to health care, food and public transport coupons, and aid for people living on pensions, as well as an increase in the minimum wage.
While the radical left Syriza government was elected on an anti-austerity platform, it is the "Troika" of the European Commission, International Monetary Fund (IMF) and European Central Bank (ECB) – much reviled among the Greek electorate – who will judge Greece's performance.
Vice-Chancellor Sigmar Gabriel said earlier on Tuesday that he was "cautiously optimistic that on Friday and today we have moved, step by step, towards a solution to the conflict".
Germany's ruling coalition between Chancellor Angela Merkel's Christian Democratic Union (CDU) and Social Democratic Party (SPD), led by Gabriel, are due to have a high-level meeting to discuss the proposal on Tuesday evening.
Eurogroup president Jeroen Dijsselbloem had earlier said that the call would only go ahead if the Troika judged the reforms went far enough.
"I think they are very serious" about the reforms, Dijsselbloem said, before adding that "it is not going to be easy. This is just a first step."
And In Berlin, German Finance Minister Wolfgang Schäuble asked the Bundestag (German parliament) to schedule time for a vote on the hoped-for deal.
Parliaments in Germany and several other countries must accept the proposals by the end of the week if Greece is to avoid missing debt repayments.
Otherwise, Greece faces bankruptcy and a possible exit from the Euro single currency, potentially costing the country's creditors, who have already bailed the country out to the tune of €240 billion plus a debt writedown of €100 billion, billions.
Elected on a platform promising an end to austerity imposed on the country from outside, Prime Minister Alexis Tsipras and Varoufakis are struggling to find a deal that can satisfy both their people and their foreign creditors.