Axel Weber was seen as a natural successor, not only because he is a German – and Germany has by far the biggest pockets in the euro zone – but also because of his hawkish stance in times when many fear that inflation is around the corner.
"After the withdrawal of Axel Weber as candidate, that has thrown the cat among the pigeons in terms of who will be the new ECB head," Michael Derks, chief strategist at FxPro, told CNBC.com.
"It is essential for the ECB to have a strong leader this time around. Germany had found that candidate in Axel Weber," Derks added.
Trichet's mandate runs out at the end of October and European heads of state and government must make a decision on his successor over the coming months.
"The market is still a little bit unsure whether it (the race for the ECB presidency) matters or not," Deutsche Bank chief international economist Stefan Schneider told CNBC.com.
Does the Top Dog Matter?
The members of the ECB Governing Council are all independent thinkers, "the top dog shouldn't matter that much," Schneider said.
But Jane Foley, a senior currency strategist at Rabobank, said both the race and Weber's withdrawal are very significant.
"The risk is now that the next member is not going to be the hawk we had grown accustomed to," Foley said.
European markets would be more reassured if the frontrunner would be German, or Dutch, somebody who could ensure that there is not going to be much of a change in the central bank's policy, she explained.
"I would expect that the ECB will remain hawkish," Foley said, adding that because the euro zone's central bank's mandate is fighting inflation the new president will have to follow that mandate.
But that mandate has come under increased pressure since last year, when the debt crisis struck the euro zone, forcing Greece and then Ireland to ask for a bailout and the ECB to do something it loathes to do: buy government bonds.
The ECB's Securities Markets Programwas created to ensure stability in financial markets and the central bank sterilizes bond purchases, therefore – in theory at least – not printing money.
It is this program that was one of the main reasons Axel Weber stepped down and there have been other signs that the central bank's independence has been threatened, Derks said.
"European politicians have been raising their expectations about what the ECB can deliver," he said. "Ultimately, they (the ECB) didn't want to be in a position where they're buying bonds."
What is needed is another strong candidate who holds the same views as Weber but who is able to build consensus, according to Derks.
At the moment, the frontrunner in the race seems to be Mario Draghi, the head of Italy's central bank the chairman of the Financial Stability Board. But Italy's high debt is seen as a disadvantage for Draghi's bid by some in the market, who fear he may be biased towards more lenience for weaker, periphery countries.
"I cannot see him looking at Southern Europe's needs and ignoring the rest," Schneider said about Draghi.
The Italian, who worked for Goldman Sachs , has first-hand expertise in financial markets, a good understanding of economy and monetary policy and of "how the political machine works," he added.