The German magazine Der Spiegel said in an unsourced report that European lenders were now expecting the IMF to contribute a sum of this size after first having hoped for 16 billion euros.
"We will not comment on speculation. The Fund's position is well known and hasn't changed," an IMF spokesman in Washington said.
It remains unclear whether the Fund will be involved in the programme, and this is likely to be one of the main talking points when German Chancellor Angela Merkel and IMF Managing Director Christine Lagarde meet next Wednesday.
Germany's government, gearing up for what is forecast to be a close-run national election in September, opposes debt relief for Greece as demanded by the IMF. Still, Berlin says the current programme can only continue if the Fund joins in.
A finance ministry spokeswoman on Friday reiterated the government's position that Berlin considers it essential that the IMF participate in Greece's third aid-for-reforms package.
The Fund has insisted on debt relief and precautionary fiscal measures to ensure that Athens can meet its fiscal targets before it will consider participating in the bailout.
Without new policies, the IMF believes Greece can only meet a primary fiscal surplus target of 1.5 pct of gross domestic product by 2018.
The Spiegel report said the IMF had now adopted the view of European lenders that Greece should post a primary budget surplus of 3.5 percent in order to get fresh aid.
In Athens, Labour Minister Effie Achtsioglou said Greece could not cut pensions any further as demanded by the IMF, drawing a line in the sand days before euro zone finance ministers assess Greece's progress in fulfilling the conditions of its bailout.
The review has been beset by delays and disputes between Greece and its European Union and IMF creditors. As disagreement has arisen over Greece's fiscal targets and reforms prescribed under its bailout programme, fears have grown that Europe could face a new financial crisis.
Greece's slow progress in carrying out reforms has been overshadowed by the rift between Germany and the IMF over the size of projected fiscal surpluses in and after 2018, when the third bailout, worth up to 86 billion euros, is due to end.
The IMF insists that Athens cannot meet the EU's target for a primary surplus of 3.5 percent of economic output in 2018 unless it adopts more austerity.
But rather than more Greek belt-tightening, the IMF says it wants the primary surplus target cut to 1.5 percent of GDP and wants significant debt relief for Athens.
Euro zone officials said last week that the lenders would ask Greece to broaden the tax base and cut pensions again, in measures which together would be worth 3.6 billion euros or 2 percent of GDP.
(1 = 0.9383 euros)
(Additional reporting by Michele Kambas and Renee Maltezou in Athens; Writing by Michael Nienaber; Editing by Hugh Lawson)
By David Lawder and Michael Nienaber