European Union finance ministers could reach a compromise on a single supervisor for European banks, Swedish finance minister Anders Borg said on Tuesday, appearing to soften his objections to giving that role to the European Central Bank.

Sweden, Denmark and Poland object to the ECB - the central bank of the euro zone - supervising all banks in the European Union, including those in non-euro zone countries, because these countries have no say in ECB decisions.

"We think there should be equal treatment to all members of the European Union that want to join the supervision board," Borg told reporters on entering a meeting of EU finance ministers that is to discuss the issue.

"There can be no unfair treatment of the non-euro countries. There must be safeguards and we must be able to set our own capital requirements, higher capital requirements for banks," Borg said.

"There could be a compromise today but there is quite a lot of road to travel. There is a long time to Christmas. We can have extra Ecofins (meetings of EU finance ministers) at any time and continue negotiations," he said.

(Reporting By John O'Donnell, writing by Jan Strupczewski, editing by Sebastian Moffett.)