"It is true that in the European Union we have not yet explored all the scenarios to help Greece," Schäuble told German business daily Handelsblatt in an interview.
He also acknowledged that "budget discipline measures by themselves cannot resolve the problems" faced by Athens as it struggles with about €340 billion ($480 billion) in debt.
But the finance minister also echoed ECB warnings about risks that could be unleashed by changing terms in the repayment of that debt, narrowing public differences with the central bank that have alarmed analysts and markets.
Such a decision could cause financial turmoil in Greece and elsewhere if investors rushed to get their funds out of the country and feared similar moves in Ireland and Portugal, ECB officials and economists have warned.
Schäuble took care to support the ECB, after media reports highlighted the danger of a clash to investor confidence in the 17-nation eurozone.
"We have always been well-inspired to respect the independence" of the central bank, Schäuble stressed.
Barclays Capital economist Frank Engels said that remark suggested "that the German government would not want to risk an open conflict with the ECB."
Berenberg Bank chief economist Holger Schmieding warned last week that Berlin and the ECB were headed for "their most serious conflict yet.
"Resolving this conflict ought to be the top political priority in Europe in the next few weeks," he added.
Schäuble had previously floated the idea of a "soft" restructuring of Greece's debts, a notion that might involve an extension of the reimbursement period or a lowering of interest rates applied to it.
Markets fear that would lead sooner or later to a "hard" restructuring, under which a substantial part of the money Greece has borrowed would not be paid back.
An aid programme worth €110 billion set up by the EU, the International Monetary Fund and the ECB has forced Greece to adopt austerity measures that will likely curb short-term economic growth.
"There must be medium and long-term growth prospects," the German finance minister told Handelsblatt, including investments in solar energy and electric power networks.
The floating of such investment in Greece marked an advance from positions by EU leaders that have focused on privatisation of Greek state holdings and economic reforms.
But Schäuble and Chancellor Angela Merkel, who have expressed different positions on the issue of restructuring Greek debt in the past, appear to be reading from the same page now.
Merkel and other EU political leaders have argued in the past that banks must share in the effort of resolving debt crises in peripheral eurozone countries, rather than having taxpayers always foot the bill.
At present, however, she too opposes debt restructuring.
The ECB is worried it could provoke a Greek bankruptcy that would plunge the eurozone into a grave crisis that would be far more expensive in the long run.
The central bank also holds some €45 billion in Greek debt and has lent money to Greek banks against much more in Greek-based collateral, and could thus suffer heavy losses if a restructuring took place.
"We thought it was time that the German government would speak with one voice and show more leadership in Europe on the matter," Barclays economist Engels said.
"We believe that today's interview by the finance minister is the first notable and important step in this direction."