Greece expects to have reached a deal “hopefully” as soon as Sunday.
A team of negotiators from Athens has been locked in talks over its €320bn (£228bn) debt pile with its creditors the European Union, the European Central Bank and the IMF since February.
It is not thought the deal will include the €20bn it owes the IMF, however.
Greek spokesman Gabriel Sakellaridis said: "We believe we are near a deal", adding that without a solution in place there would be "wider consequences for the EU", not just financial issues.
Without a deal in place the country faces default or bankruptcy, and almost certain expulsion from the single currency union.
Greek two-year yields, which had reached dangerously high levels, have plunged on the news. 10-year yields have also fallen.
Yesterday Greek prime minister Alexis Tsipras confirmed speculation that a deal was on its way, following reports that the parties had started procedures to draw up a staff-level agreement.
However anonymous officials appeared sceptical about the news, telling Reuters it was "nonsense" or "I wish it were true".
That cynicism is being shared on Twitter:
Greece wants a deal by Sunday. And a pony.— Gustavo Baratta (@gusbaratta) May 28, 2015
But European Commission spokeswoman Annika Breidthardt is reported as saying there are still several "open issues" that need to resolved before a deal is signed.
"Further progress is needed," she said, adding: "We're not there yet."