The cuts will be done through layoffs, moving staff, or not filling vacancies and will be implemented by the end of the year, the newspaper reporter.
The 30-year-old airline is looking to boost earnings after it reported a 14.4 million pounds (US$22.62 million) profit for 2014, its first in four years.
Virgin is in the throes of a two-year turnaround plan that includes shutting its Little Red domestic airline to concentrate on long-haul flights.
The airline is increasing its transatlantic flights while cutting back on some routes elsewhere. It is also contemplating how to replace seven Boeing 747s it flies from London's Gatwick Airport, and could expand its overall fleet in the process.
Virgin Atlantic was not immediately available to comment on the report.