Greece and its creditors were involved in "intense talks" over the weekend to agree a new bailout before the debt-ridden country must repay 3.4 billion euros ($3.7 billion) to the European Central Bank on August 20.
European officials said sticking points still remain despite the progress being made, with a "generally positive reception... towards Greek readiness to vote on reforms this week.
"It is ambitious but feasible to come to an agreement in the coming days, preferably by 20 August," an EU diplomat said Saturday.
Greece has been in discussions with officials from the ECB, the IMF and the European Stability Mechanism for the past week over further reforms they are demanding in return for a third bailout for up to 86 billion euros.
With its lenders insisting on "very good co-operation" from Athens, both sides were "working flat out on a draft memorandum of understanding" and "intense talks with Greece will continue over the weekend," another EU source said.
The ECB deadline means an agreement will have to be reached by next Monday to prevent Greece having to ask for a bridging loan to stop it defaulting on another repayment.
Cash-strapped Greece already missed two key payments to the International Monetary Fund that were due on June 30 and July 13, but the repayments -- amounting to around two billion euros -- were later made possible with a short-term EU loan.
Greek Prime Minister Alexis Tsipras said Thursday that the talks for a new bailout were in the "final stretch".
Tsipras is under pressure from a sizeable minority in his radical-left Syriza party who say the rescue package he agreed to in July piles further austerity on a weakened economy and goes against the government's campaign pledges.
But European Commission President Jean-Claude Juncker was optimistic a further crisis could be averted. "All the reports that reach me leave me to believe that an agreement will be possible in August," he told AFP.
Berlin, whose hardline stance forced Greece to cave in and accept further austerity measures, did not hide its doubts, however. Officials made clear earlier this week that there were "still a number of points to clear up".
According to the Sunday edition of the German Frankfurter Allgemeine Zeitung, a 27-page draft memorandum of reform commitments must be signed off by the Greek government this weekend to allow the new bailout to go through before the August 20 repayment falls due.