The Hellenic state faces a debt repayment in July that amounts to around €7.4 billion.
Schaeuble, a member of Chancellor Angela Merkel's conservative Christian Democratic Union party, has recently clashed with politicians from Germany's Social Democratic Party over his refusal to sign off on more payments to Greece without the International Monetary Fund.
"That will be one of the hard issues, we have had many preparatory talks, but I'm confident we can find a solution", he said.
One person involved said planning debt relief based on the most pessimistic International Monetary Fund forecasts would lead to Greece not paying off some bailout debts until after 2100, an outcome no one is seriously considering.
But Macron's position puts him at odds with Germany where Greek debt relief, following three different bailouts since 2010, is seen as a vote loser ahead of general elections in September.
"I hope that we will reach a solution today that ends this politically", Schaeuble said on his way into the meeting. It is also important to restore investor confidence in Greece, especially if the country, which has public debt of nearly twice the size of its GDP, is to return to market financing.
The Brussels-based meeting was aimed at deciding whether Greece had done enough to receive a €7.5bn (£6.4bn; $8.3bn) loan plus debt relief.
Ministers did not agree on releasing new loans to Athens, but Jeroen Dijsselbloem said work was progressing towards a next disbursement "before the summer".
The new delay on fresh aid and debt relief will infuriate the Greek government, which pushed through the tough reforms to be ready for Monday's talks.
IMF's Head of the European Department Poul Thomsen said on Tuesday that both sides did make progress in debt talks, but "we are not quite there yet".
The IMF and Germany disagreed over Greece's economic outlook and the amount of debt relief required to assure economic stability, according to two European Union officials with knowledge of the talks, who asked not to be identified because the discussion was private.
Dijsselbloem said he expected a deal to be struck between Greece and its creditors at the next Eurogroup meeting in June.
Analysts said the main reason why Greece has taken a step back is its stalled bailout negotiations.
One potential ally for Greece is Emmanuel Macron, France's new president.
Greek Prime Minister Alexis Tsipras and German Chancellor Angela Merkel agreed during a call on Wednesday that a deal was "feasible" by Monday.
The IMF believes that debt relief, or at least a clear promise of it now, is needed to restore investor confidence in Greece, especially if the country, which has public debt of 197 percent of GDP, is to return to market financing next year.