Spokesman Luc Chatel told France's Radio-J an investigation is under way and insists the incident "proves that this system of checking (bank accounts) via the Internet isn't infallible."
"We will see if there was fraud in a way in which the perpetrators can be sanctioned," he added.
It "is not excluded" that Sarkozy's bank might some of penalty over "misuse of personal data," Chatel said.
"When one gives personal information to one's bank, it is not so the information is used for marketing or recruiting purposes, or that it should be divulged here or there," he added.
Weekly Journal du Dimanche reported Sunday that thieves seized Sarkozy's bank account information and swiped small sums of money.
The newspaper said Sarkozy reported the theft last month and that those responsible haven't been found. The report cited an unnamed official close to the investigation for its information.
The failure to apprehend the criminals "shows that the criminals weren't amateurs," wrote the newspaper.
The press service for Sarkozy's office declined comment.