The former Southern Cal running back would become the first player in the 75-year history of the award to have the Heisman Trophy taken away. The report also says the award would be left vacant for '05.
The NCAA found major violations in USC's football program and levied serious sanctions against the school in June.
The website on Tuesday cited two anonymous sources close to the Heisman Trophy Trust, who say the group's investigation is almost complete and would agree with the NCAA's finding that Bush was ineligible during the '05 season.
Bush now plays for the Super Bowl champion New Orleans Saints.
