The euro slipped to $1.3417 on the speculation, although by midday Thursday in London it had recovered to trade at $1.3466 following comments by Draghi playing down the reports.
Bank of Tokyo-Mitsubishi's Hardman said that although the euro sell-off may not extend much further in the near-term, it reflected speculation that the ECB will have to ease its monetary policy further.
"With conventional easing measures almost exhausted, this is encouraging speculation that the ECB will have to adopt more unconventional measures such as lowering the deposit rate into negative territory," Hardman said, given the weak growth and low inflation outlook in the euro zone.
And in a recent report on currencies HSBC's Global Head of FX Strategy David Bloom agreed, saying that further monetary easing was likely in the euro zone.
"Fortunately, the ECB has potential medicine at hand to try and reduce the pain being inflicted by the stronger EUR," Bloom wrote in a recent currency report.
He highlighted that although much has been made of the euro zone's recovery, it is getting increasingly unlikely that there will be any more good news surprises in the near future.
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"It is hard to isolate the role of the stronger euro in these more recent disappointments but it is clear that net exports have been an important part of the recovery story," Bloom wrote.
Germany – the euro zone's largest economy which has been powering ahead as its neighbors struggle – has been accused of hitting the chances for recovery of its fellow euro countries by having a strong export market and budget surplus.
Indeed, Rabobank's Foley said it was Germany's strength that was lending the euro support.
"Germany is helping the euro zone lose the currency war, on the assumption that currency weakness is the desirable result," she told CNBC.