The Financial Times Deutschland, quoting sources in Brussels and other European capitals, said Merkel has been lobbying other government chiefs for Schäuble, 69, to take over from Luxembourg Prime Minister Jean-Claude Juncker when he steps down in June.
Schäuble was seen as having the best chances at the moment after other potential candidates such as Italian Premier Mario Monti and Finnish Prime Minister Jyrki Katainen have turned the job down, the newspaper quoted the sources as saying.
But there was resistance in Paris, where President Nicolas Sarkozy was concerned that Germany's position would become too strong, it added.
A finance ministry spokesman in Berlin declined to comment on the report.
"We don't comment on the nomination process," he said, adding that the matter was not pressing and would probably be decided in May at the same time as other appointments to the European Central Bank and the European Bank for Reconstruction and Development.
Schäuble himself similarly refused to be drawn into making any comment.
"We have other issues at the moment. Speculation about personnel matters might be interesting for the media, but there are other issues facing us," he told reporters at a news conference in the German capital.
"If Mr Juncker is no longer available for the post, then we're going to have to look at this question in time. But that is all for today," the minister said.
Juncker has suggested that the position of Eurogroup chief be turned into a full-time job. But Germany believes that the post should be held by a minister in office, the finance ministry spokesman said.
Schäuble's current term as finance minister for Europe's biggest economy is to expire in the autumn of 2013 when the next general elections are held in Germany.