"I think the general picture is that we are on target to have a conclusion on May 22," Tsipras said in Brussels, referring to a scheduled meeting of eurozone finance ministers needed to approve the deal.
Greece's creditors -- the European Commission, European Central Bank and the IMF -- on Tuesday resumed a long-delayed audit that is required for any agreement.
Disputes remain on reforms including labour rights and the breakup of Greek near-monopoly electricity provider PPC -- both thorny issues for Tsipras' leftist-led government.
Under pressure from its creditors, Athens earlier this month accepted to reduce pensions in 2019 and lower tax breaks in 2020.
These measures are worth around 3.6 billion euro (USD 3.8 billion).
However, Tsipras has said he will not apply these cuts without a clear pledge later this month on debt-easing measures for Greece.
Athens also hopes to be finally allowed access to the European Central Bank's asset purchase programme, known as quantitative easing, or QE, to help its return to bond markets.
But the IMF has so far refused to take part after two prior programmes on the grounds that the targets were unrealistic and Athens' debt mountain was unsustainable.
A compromise is required to unblock a tranche of loans Greece needs for debt repayments of seven billion euros in July.
Additional debt relief for Greece has proved a contentious point for many of its European creditors including Germany, where additional concessions are unpopular with an electorate called to a general election in September.
Eurogroup head Jeroen Dijsselbloem this week said a deal to break the deadlock over Greece's bailout "needs to be done in May".
"The situation in Greece is not good enough. Growth is falling back again," he said.
"Debt relief will be needed to find a solution. That's my opinion and I belive that is shared in the Eurogroup," Dijsselbloem said.
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