Speaking at a two-day meeting of EU finance ministers in Nice, Steinbrück voiced his concern about the struggling bank, which is attempting to form a buyout plan in order to avoid becoming the latest victim of the global credit crisis.
“The news from the United States is bad,” he said with regard to the turmoil stemming from the US subprime mortgage sector.
Speaking specifically about Lehman Brothers, he told reporters. “We expect a solution to be available and announced before the Asian markets open on Monday. Don't ask me what it will look like, I am not involved (in the negotiations).”
The president of Germany's central bank, Axel Weber, said that the crisis engulfing Lehman Brothers marked "another round of tension in the markets" after the collapse of Bear Stearns earlier this year.
The travails of big US financial institutions like Lehman Brothers, Freddie Mac and Fannie Mae has focused the minds of Europe's finance chiefs on whether they are prepared to react in case a major European bank also runs into serious trouble.
Although national governments have their own plans if a local bank hits the rocks, Europe still lacks a prepared response in case of problems at a big pan-European bank.
European financial regulators have failed to keep up with the waves of cross-border consolidation in the banking industry sector in recent years, leaving banks largely supervised along national lines.
That leaves big European banks like Deutsche Bank, Unicredit or BNP Paribas facing a hodge-podge of regulations across Europe, which officials fear could be a burden if ever there were serious trouble.
In Europe, the bailout of institutions as big as Freddie Mac and Fannie Mae would be made all the more difficult because governments would want to limit contributions of taxpayers' money, especially if the bank were based in another country.
Despite the extreme stress gripping the sector, EU central bankers are mostly confident that European banks can resist.
With Lehman Brothers still in dire straits on Saturday, Germany's Weber said that at least for German banks "the consequences will be limited" if the US investment bank avoided a catastrophic end.