This unconventional policy—which means banks are charged interest for holding money with the central bank—was introduced in June 2014 in yet another effort to incentivize banks to lend money to businesses and consumers, rather than park it with the ECB.
But Major said that QE and negative deposit rates at the central bank (currently at -0.2 percent) were "mutually exclusive," despite similar intentions behind the policies.
"I don't get how they (the ECB) are going to buy a lot of bonds when the (deposit) rate is -20 basis points, because the banks are not incentivized to play," Major told CNBC on Tuesday.
"Why would a bank give up a bond, which it holds for a perfectly good reason, and give it to the ECB and get -20 basis points for a risk-free asset?"
Read MoreBond yields sink below 2% in flight-to-safety bid
One way for the ECB to get around this would be for the central bank to purchase bonds at a premium in order to compensate for its own negative deposit rate. Alternatively, the ECB might buy bonds directly from asset managers, said Major, skipping the banks altogether.
Despite concerns about effectiveness, recent weak economic data for the euro zone is seen as upping the chances of ECB QE. On Tuesday, Markit's much-watched composite Purchasing Managers' Index (PMI) came in weaker than expected for the euro zone, indicating that business activity grew at a slower rate than forecast.
Read MoreEuro zone economy ended 2014 on low note
Uncertainty about the ECB's next move, along with political woes in Greece, continue to weigh on European markets. Since the start of the year, the pan-European Euro Stoxx 600 has fallen roughly 3 percent.