Bloomberg reports that chiefs are finding it difficult to convince investors that they can come up with a suitable bailout.
European Union (EU) leaders are due to meet on 21 July 2011 in an attempt to move forward with a plan of action - the second such gathering in a month.
However, dissenting voices appear unconvinced that a breakthrough will be made.
Suki Mann, senior credit strategist at Societe Generale - which has been in operation for more than 140 years - said there have been "few soothing words" concerning the matter.
The industry figure added: "Greece appears beyond repair, Italy is on the brink and the chances are that the euro might be no more very soon."
EU president Herman Van Rompuy called for the Brussels meeting to give European chiefs the opportunity to discuss the financial stability of the euro as a whole.
By Claire Archer