First, Europe stress tests… Next, full QE?

Following the results of Europe's bank stress tests, there are growing calls for the European Central bank (ECB) to start buying sovereign bonds in an effort to stump up the region's flagging recovery.

The ECB has already launched a host of stimulus measures to reverse growth-sapping disinflation, including cutting interest rates to record lows and announcing plans to purchase covered bonds and asset-backed securities (ABS).

Many economists have warned this is not enough, however, with former ECB Governing Council member Athanasios Orphanides telling CNBC that the central bank "should have already started" buying sovereign bonds—or full-blown quantitative easing (QE).

Read MoreECB stimulus may lack desired scale, QE an option: Sources

"Now that the stress tests are out of the way, it would be quite positive for the euro area if they announced that move as soon as possible," Orphanides said late Wednesday.

Euro logo sign European Central Bank ECB Frankfurt Gerrmany
Ralph Orlowski | Reuters

On Sunday, the ECB revealed that 25 European banks had failed the stress tests and exposed a 25 billion euro ($31.7 billion) shortfall on their books. The results of the tests - a key healthcheck of the region's financial system – had been awaited with bated breath, and Orphanides said that now the findings were published, it was time for the ECB to "adopt vastly more expansionary policy".

Read MoreECB tests fail 25 banks with $32B shortfall

"It's not clear to me why going forward, with the announcement of the stress tests, the Governing Council of the ECB would not now take the necessary action to increase the size of its balance sheet, which I believe will necessarily include purchases of government debt," he added.

Unlike central banks in the U.K., U.S. and elsewhere, the ECB has not launched a full-blown QE program – mainly because there are no common euro zone bonds and the process of picking which country to buy is fraught with political dangers. Such a move has also been openly opposed by Germany's Bundesbank – the largest country-specific central bank in the region.

But a number of economists are calling on the ECB to overcome these hurdles in an effort to reignite its stagnant economy. One of the most concerning symptoms of a struggling euro zone is persistently low inflation, which fell to just 0.3 percent in September. The region is also battling no growth – with gross domestic product (GDP) coming in flat in the second quarter – and a stubbornly high unemployment rate of 11.5 percent.

Given this bleak economic picture, there are market rumors that the ECB is considering buying corporate bonds to expand its balance sheet further and pump liquidity into the market.

But few are convinced that the market is large enough – even combined with the purchase of ABS – to boost the central bank's balance sheet by the required amount.

"Rumors that the ECB is considering corporate bond purchases suggest that the bank is edging further into the realms of quantitative easing," Jennifer McKeown, senior European economist at Capital Economics, wrote in a note. "But we think that it will need to buy sovereign bonds as well to ensure a meaningful expansion of its balance sheet."

Read MoreCentral bankers back stress tests as criticism swirls

Deutsche Bank economists led by Marco Stringa agree, arguing that the purchase of corporate bonds will not be a game changer.

In September, Stringa called for full QE within six months, and last week added that: "Recent concerns about global growth and evidence of a slowdown in the already-weak euro-area recovery have strengthened our call."

"Hence, in our view the ECB will have to broaden its asset purchase program," he said, adding that only government bond purchases "would provide a large and liquid enough pool to lift inflation close to the 2 percent target in 2017".

For Orphanides, such a move was necessary – and should be implemented now – in order for the euro zone to avoid a return to recession, warning that "inaction can be incredibly costly".

"We may have a triple dip in the euro area – and we're barely out of the second dip," he said. "If the ECB were to act very quickly in order to meet its price stability mandate I think that would provide sufficient accommodation so that even if we have continued declines for the next few months they would be quickly reversed."

- By CNBC's Katrina Bishop