The newspaper reports Air France-KLM management is counting on 800 people leaving the company through normal attrition, but will also open a voluntary buyout offer for all personnel, including pilots.
But an Air France-KLM spokesman said negotiations with labour unions to find ways to reduce costs were still underway and no announcement on jobs was expected until the end of June.
"The economic situation at Air France is worrying, notably because of a significant lack of competitivity," the spokesman told the French news agency. "But a reform plan intended to regain competitivity by 2015 continues at management level as well as with the worker representatives management is currently in discussion."
Another French news media, La Tribune.fr, said the buyout offer would affect 2,500 to 3,000 jobs.
On Thursday Air France-KLM chief executive Alexandre de Juniac is due to report progress made on a three-year turnaround strategy announced in January.
The cost-cutting plan, including wage freezes and investment reductions, aims at saving at least two billion euros and reducing debt.
Air France-KLM aims to reduce its net debt by two billion euros to about 4.5 billion euros by the end of 2014.