It cited no sources for the information in a summary of a story released ahead of publication on Thursday.
Julius Baer declined comment on the report, but said:
"Julius Baer -- as one of several banks mentioned in the FIFA indictment through which allegedly incriminated transfers had been transacted -- has launched an internal investigation and is cooperating with the authorities. As a matter of policy, we do not further comment on pending proceedings."
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U.S. prosecutors in May indicted 14 soccer and marketing officials in the biggest corruption inquiry to hit FIFA in its 111-year history. Switzerland's Office of the Attorney General (OAG) is conducting a parallel investigation.
The OAG had by last month gathered around 11 terabytes of electronic data and 121 different bank accounts had been flagged for suspicious activity.
The OAG said in August it had received 103 suspicious financial activity reports for its inquiry.
Handelszeitung said Swiss banks had reported suspicious activity by around 50 clients in the case.
(Reporting by Michael Shields and Oliver Hirt; editing by Ralph Boulton)
