German Chancellor Angela Merkel says she could back a eurozone finance minister and eurozone budget "if the circumstances are right".
French President Emmanuel Macron has argued strongly for both, in order to reform the eurozone.
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.
"We could also consider a euro-budget if it is clear that we are really strengthening the structure of the economy and doing sensible things," she said.
President Macron's strongly pro-EU stance has boosted Mrs Merkel's position in the run-up to Germany's general elections in September.
But reforming the eurozone remains a major challenge. The 2008 financial crash and subsequent eurozone debt crisis led to high unemployment and painful public sector cuts in much of Europe.
Merkel strikes a balance - Jenny Hill, BBC News, BerlinImage copyright AFP Image caption Mr Macron and Mrs Merkel are looking ahead to a more closely integrated EU - without Britain in it
The old French-German alliance that once powered the political heart of the EU is spluttering back into life, fuelled in part by Britain's decision to leave the union.
Angela Merkel and Emmanuel Macron share a vision of an EU of closer integration, stronger co-operation.
It's a vision which rather appeals to German voters too. But they (and consequently Mrs Merkel) are rather more wary of his ideas for the future of the eurozone. Germans, still smarting from the Greek debt crisis, are sensitive about the idea of their money bailing out other countries.
So Mrs Merkel is treading carefully, ensuring that her support for a eurozone finance minister and possibly a budget too was counter-balanced with the apparent insistence that there could be no mutualisation of individual state debt.
She's striking a balance, forging an alliance with Mr Macron but keeping a close eye on the German electorate.
And - while it's unlikely to have been deliberate - the timing of her comments come just as Brexit negotiations begin. She's been keen to steer that narrative towards the future of the EU without Britain; raising the prospect of closer fiscal integration among eurozone members may help to achieve that aim.