Berlin would "view positively" such a move, the source said after another European source close to the matter told news agency AFP that ECB governors would discuss the issue at a regular meeting on Thursday.
"I cannot rule out that (ECB President Jean-Claude) Trichet will bring this up. Germany has always said it would support the ECB," the Berlin source said.
"This capital increase ... would be for markets to see that the ECB is well capitalised if it buys more bonds."
The ECB's capital currently stands at almost €5.8 billion ($8 billion). Press reports said a capital increase would strengthen the ECB's safety net as it deals with risk linked to purchases of public debt issued by weaker eurozone countries like Greece, Ireland and Portugal.
The ECB is pressing political leaders to boost the size of a fund created to preserve financial stability, two days ahead of a crucial European Union summit.
"We are calling for maximum flexibility, and I would say maximum capacity, quantitatively and qualitatively," for the European Financial Stability Facility (EFSF), Trichet told the media in Frankfurt late on Monday.
On Thursday and Friday, EU leaders are expected to approve a permanent eurozone crisis fund that Economics Affairs Commissioner Olli Rehn said will provide a "systemic" response to the eurozone debt and deficit crisis.
Bond markets have targeted several weaker eurozone countries including Ireland and Portugal in the fallout from the Greek debt crisis in May. The ECB has bought government bonds as borrowing rates for those members soared, marking another stage in the crisis, but raising questions as to how far it could go with this tactic.
Trichet said that "crises of that amplitude call for all of us in Europe to reflect intensively on what should be done" and urged EU leaders to do more than they have offered to so far.
In particular, deadlines for action by governments running excessive public deficits should be shortened and sanctions should be applied in a way that is quasi automatic and based on clearly defined criteria.
EU politicians that are supposed to keep an eye on each others' finances have considerable say in such matters but have in the past been reticent to approve painful sanctions on each other.
Trichet has called several times for governments to make a "quantum leap" in governance in response to the crisis and said he believed they would rise to the challenge owing to pressure being brought by emerging economies.
"The changes I see in the rest of the world over the last 20 years are in my opinion confirming that the deepening of European unity is more justified than ever," he said.