"Luckily, Greece is no threat to the world economy," Asmussen told the Financial Times Deutschland.
"Nevertheless, other countries expect us to find a solution. But by the G20 meeting at the end of the week, we'll be a great deal further" towards one, he said.
Eurozone finance ministers are meeting in Brussels on Monday to finalise a second Greek bailout in a deal which they hope will also quell suggestions that Greece could be pushed out of the currency area.
The deal to write off €100 billion ($130 billion) of debt and provide loans worth another €130 billion is contingent on painful new spending cuts that Athens must make despite violent protests.
Finance ministers and central bankers from the Group of 20 countries are to meet in Mexico City on February 25-26.
In a separate interview with the business daily Handelsblatt, the ECB's director general for legal services, Antonio Sainz de Vicuna, said the bank was looking into ways for eurozone governments to channel profits from the ECB's holdings of Greek bonds to help Greece.
"There is the political wish for the profits that we make on the bonds to be distributed to the EFSF (European Financial Stability Facility)," the EU's bailout fund, Sainz de Vicuna said.
Story continues below…
"Whether and how this can be done hasn't been agreed yet," he said, while insisting that the ECB itself is forbidden from financing governments. "That is a political decision, but the eurosystem must possibly agree to it to ensure that the procedure is in line with the law," he said.