German Chancellor Angela Merkel said new proposals offered by Greece constituted ?some progress?. But she said more work was needed and ?time is short?.
Greece must repay a ?1.6bn (?1.1bn) International Monetary Fund (IMF) loan by the end of the month.
If it fails to do so, it risks crashing out of the single currency.
Although no deal has been struck, key obstacles appear to have been cleared, BBC Europe Correspondent Damian Grammaticas reports from Brussels.
The deal being formed is said to include:
New taxes on businesses and the wealthySelective increases in VATSavings in pensions linked to curbing early retirement and increasing employer pensions contributionsNo further reductions in pensions or public-sector wages ? ?red lines? for Greece?s Syriza government
Only once agreement is reached will creditors unlock the final ?7.2bn tranche of bailout funds.
The move was received with cautious optimism by leaders of 18 other eurozone nations gathered for an emergency summit in Brussels.
Greek Prime Minister Alexis Tsipras met the heads of Greece?s three international creditors ? the IMF, the European Commission and the European Central Bank (ECB) ? in Brussels on Monday ahead of attending the summit.
After the talks ended on Monday evening, Mrs Merkel said that everyone taking part wanted Greece to stay in the eurozone, ?myself included?.
?The proposals offered by Greece today constitute some progress. However, it became clear during our discussions that there is a lot of work to be done and time is short,? she said.
French President Francois Hollande said Greece and its creditors were ?moving towards an accord?.
He also said there was ?still work to be done? for a solution to be in sight when eurozone finance ministers meet again on Wednesday ? when they hope to approve a package to be put to eurozone leaders for final endorsement on Thursday morning.
European Commission President Jean-Claude Juncker ? one of the key power-brokers ? told a late-night news conference: ?I am convinced that we will come to a final agreement in the course of this week?.
However, German Finance Minister Wolfgang Schaeuble was more negative about the prospects of a deal, saying he had seen nothing new from Athens.
And there was some pessimism from Greece itself, with deputy parliament speaker and Syriza lawmaker Alexis Mitropoulos reportedly telling Greek TV that lawmakers would find it ?difficult to pass? the latest package of reforms.
Meanwhile, thousands attended a rally outside the Greek parliament in Athens on Monday in support of Greece staying in the eurozone. It came a day after an anti-austerity protest backing the government?s tough stance towards creditors.
Talks have been in deadlock for five months with Greece?s three main creditors unwilling to unlock the final instalment of bailout funds until Greece agrees to economic reforms.
Greece?s left-wing Syriza government has opposed reforms that it says will impose unnecessary hardship on the Greek people.
The European Central Bank (ECB) again increased its emergency funding for Greek banks on Monday after anxious savers withdrew more than ?4bn in recent days.