Also, any "monetary financing" of governments by the ECB is also banned by European Union - another key stumbling block for the central bank launching a QE program of this sort.
What about the private sector?
Another option open to the ECB is allowing banks to parcel together loans on their books into saleable instruments called asset-backed securities (ABS). The ECB could then buy these ABS, freeing up capital for the banks.
However, ABS have a somewhat tarnished reputation -- wild trading in these instruments helped spark the 2008 financial crisis. Plus euro zone countries have different amounts of asset-backed securities, and there are difficulties in assessing their risk and price.
What the experts think
BNP Paribas economists, led by Ken Wattret, have argued for some time that "ECB QE is coming", as other measures cannot deliver sufficient clout.
The economists forecast the ECB will announce an initial program in the range of 300-500 billion euros ($415-$690 billion) – although they stressed that predicting the size of the program is "more of an art than a science."
Acknowledging the difficulties in a private sector program, however, the BNP Paribas economists added: "We conclude that some such (private sector asset) purchases are likely (and will be beneficial) but that, like other central banks, the ECB will also have to use the sovereign debt markets to find the depth and liquidity required for purchase programs of meaningful size and impact."
Read MoreQE from ECB? May not be the panacea many hope
Goldman Sachs analysts led by Huw Pill, however, said the likelihood of a Fed-style large-scale asset purchase program remained small, as the purchase of sovereign assets would "raise questions about the ECB's legitimacy in introducing a fiscal union through the back door".
He also queried the effectiveness of a QE program on yields, given that sovereign yields are already very low, even in peripheral countries.
"This is consistent with the experience of the Bank of England's QE programs, which suggests that the effectiveness of purchases falls once yields are very low," he wrote in a note.
Carsten Brzeski, senior economist at ING, said he expected a "big QE bazooka" to remain in the closet, for now at least.
"The ECB is caught between the high expectations it created and concerns about unprecedented measures such as QE being too risky and controversial to really test them," he wrote in a note.