The EU summit started Thursday, and some officials said major changes to the group's treaty is the last thing most of its 27-member group wants, The New York Times reported.
German Chancellor Angela Merkel, with support from French President Nicolas Sarkozy, has demanded alterations to the Lisbon Treaty, less than a year old, to strengthen management of the euro, the report said.
Merkel and Sarkozy announced their desire to change the treaty last week at Deauville, a French seaside resort, and the proposal has prompted a backlash from other members.
In the Deauville declaration, France agreed to support a change to the EU treaty while Germany accepted France's call to water down proposals to punish nations that fail to control their finances, the newspaper said.
Any treaty alteration would require approval from each of the EU's 27-nation membership, the report said.
"One cannot take a walk on the beach and, suddenly, announce you have found the way to save the euro -- you cannot proceed like that," said Joachim Fritz-Vannahme, director of European projects at Bertelsmann Foundation, a German research institute.
Merkel said treaty changes are necessary to set up a permanent mechanism to support euro-zone nations close to default, and to put insolvency procedures in place.