Last week German Finance Minister Wolfgang Schaeuble had clashed openly with his French counterpart Pierre Moscovici over key elements of the plan, but with time running out to meet a year-end deadline, they narrowed their differences, raising hopes of a breakthrough.
Agreement on a common supervisor is a crucial first step towards a broader "banking union", or common euro zone approach to dealing with failing banks that in recent years have dragged down countries like Ireland and Spain.
"We think that we have a good chance to reach a deal today," Schaeuble told journalists ahead of a meeting in Brussels with his European Union peers. "My intention is that we find a solution to the union on time before Christmas."
Moscovici told his colleagues in the meeting that "all the parameters" for an agreement were in place.
Even if the bloc is able to settle most of its differences on Wednesday, other difficult issues remain.
Countries like France, Italy and Spain are keen for those powers to be in place as soon as possible. But Germany, worried it could be forced to foot the bill for struggling banks across the bloc, is not in a rush.
In introductory remarks at the meeting, Schaeuble tried to kill any discussion about bank recapitalizations and said it could take more than a year for the new supervisor to be fully up and running.
In the longer-term, there is disagreement over how the burden of winding down failed banks should be shared.
A compromise document put forward by rotating EU President Cyprus, and obtained by Reuters on Tuesday, won broad backing at the meeting from the ECB and member states.
In recent weeks, Germany had argued against giving the ECB supervisory responsibility for all 6,000 European banks, concerned the new system could become unmanageable.
The new proposal recommends that banks with assets of 30 billion euros, or larger than one fifth of their country's economic output, be supervised directly by the ECB rather than national supervisors.
Critically, it also gives the ECB authority to widen its remit to smaller banks if problems arise.
But the tone of Wednesday's gathering was a far cry from a meeting last week intended to finalize the plan when Schaeuble clashed with Moscovici. France wanted a broad ECB remit, while Germany had reservations.
Schaeuble had objected to the ECB's Governing Council having the final say over monitoring banks, but said at the meeting on Wednesday that he thought a compromise could be found.
Reaching a deal, which EU leaders hope to sign off at a summit on Thursday and Friday, will also require the backing of others with vested interests such as Britain, Sweden, Poland, Hungary and the Netherlands.
Sweden's Finance Minister Anders Borg spelled out his objections to peers, saying there was no way for non-euro countries to participate in the ECB-led scheme on an equal footing with countries in the currency.
He said that Sweden was unlikely to join but could allow the banking union go ahead for others, although he warned it could create "substantial division" in the European union.
Britain has similar worries, although its finance minister signaled at the meeting that a deal was possible.
George Osborne said one of his main concerns was avoiding a situation where the ECB might infringe on Britain's autonomy in monitoring the City of London, Europe's biggest financial centre.
"It would be very difficult for us to accept that the ECB could exercise certain powers for Deutsche Bank in London. That would be an unfair arrangement," Osborne said.
All 27 EU states must give approval for the project to go ahead, even if only those countries in the euro zone will fall under the banking union to begin with.
Under the Cypriot proposal, the ECB's Governing Council would keep the final say in supervision, but it also lays emphasis on the need for a clear operational separation between monetary policy and supervision. In a nod to Germany, it says the new supervisor may not be fully operational until April, 2014.
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