On Friday, Draghi reiterated that the ECB was committed to expanding its asset purchase program -- a move that many market-watchers expect could include euro zone government debt.
"We are committed to recalibrate the size, pace and composition of our purchases as necessary to deliver our mandate," he said.
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"This is why the Governing Council has tasked ECB staff and the relevant Eurosystem committees with ensuring the timely preparation of further measures to be implemented, if needed."
However, Draghi may face opposition from more hawkish members of the ECB's Governing Council, including Jens Weidmann, the president of Germany's central bank. Weidmann has previously warned of the "dangerous path" that quantitative easing (QE) would lay. He will speak at the European Banking Congress on Friday.
Phillippe Legrain, former economic advisor to ex-president of the European commission, Manuel Barroso, said that markets were overestimating the possibility of QE taking place.
"There is deep opposition to that and in the context of an ECB which is very sensitive to German opinion... I don't think that QE in the bold way that is necessary is going to be carried out in the euro zone," Legrain told CNBC before Draghi spoke.