German Chancellor Angela Merkel says she could back a eurozone finance minister and eurozone budget "if the circumstances are right".
Germany is wary of any move that might lead to a "transfer union" - a common budget used to prop up indebted governments in the 19-nation eurozone.
Many Germans resent the billions of euros spent on bailing out Greece.
The Berlin government does not want German taxpayers to have to underwrite high spending elsewhere in the EU without oversight.
Mrs Merkel said sensible changes could be introduced if they could be sure of improving the lives of European citizens, including generating work for young people. She was addressing German business leaders in Berlin.
Read more: Merkel reaches out to France's Macron on eurozone budget - BBC News