The ESM is now an intergovernmental body, operating on the basis of a treaty between the 19 countries sharing the euro. Integrating it into the wider EU law would make it an EU, rather than just a euro zone institution.
Most euro zone governments oppose it on concerns of losing full control over the funds' 500 billion euro lending capacity.
"The ECB supports the European Commission's initiative to bring the European Stability Mechanism (ESM) into the Union legal framework," the ECB said.
"This initiative is an important step towards the completion of Europe's economic and monetary union," the ECB said.
"The establishment of the ESM as a body of the Union would allow it to better achieve its objective of contributing to safeguarding the financial stability of the euro area, as well as of the Member States participating in the banking union."