Speaking as he announced plans to curtail the pace of its bond buying program, Draghi said Thursday that the vulnerabilities of Monte Dei Paschi as well as Italy's banking system as a whole would be resolved by the country's government.
"They (issues in the banking system) will be dealt with," Draghi said.
Monte Dei Paschi had previously asked the ECB on Wednesday for five more weeks to complete its 5 billion euro ($5.4 billion) rescue plan.
The oldest lender in the world has claimed that the ongoing political instability in Italy has not enabled it to raise the money it needs to finance its operations. A deal, that was expected to be concluded in December, may not be ready until a new government is in place.
Investors are waiting for clarity on whether the Italian President, Sergio Mattarella, will order a new technocratic government to take over or call for snap elections.
Mattarella began talks on Thursday with political leaders in a bid to find a way out of the current political crisis caused by voters rejecting constitutional reforms at the country's recent referendum and Prime Minister Matteo Renzi's resignation.
The ECB is expected to make a decision on the extension request on Friday. For now, it remains unclear which direction the central bank will take. Monte Dei Paschi has failed the ECB's stress tests twice and its fragile state threatens not only the Italian banking system but also the euro zone.
The International Monetary Fund (IMF) said last July that Italian banks "face significant challenges from weak asset quality and low profitability" and these problems aren't new. In November of last year, four small Italian banks were recapitalized under previous EU rules.
If the ECB does not approve the extension until mid-January, the Italian government will need to carry out a state bailout, which could raise issues regarding state aid.