The revelation suggests the government is ready to commit to a far bigger -- and inevitably far longer -- role in the campaign against Islamist groups in northern Mali than previously indicated.
President Francois Hollande said earlier on Tuesday that there were currently 750 French soldiers in the former colony but acknowledged that this figure would increase.
"There will be a gradual build-up to a figure of 2,500," a source close to Defence Minister Jean-Yves Le Drian said.
The plans to deploy a force of that size is at odds with suggestions by government ministers that the involvement of French ground troops would be limited to protecting Mali's capital, Bamako.
According to Le Monde and other French media, France is also planning to base a substantial contingent of troops at Mopti in central Mali, from where they will be able to carry out operations in the north of the country.
Until now, ministers have portrayed France's involvement as restricted to stopping the Islamists' push south with the subsequent task of regaining control of the north to be handed over to the Malian army with the support of troops from neighbouring West African states.
Military analysts have described this scenario as optimistic given the limited capacity of the Malian army and the West African forces lack of experience in combatting battle-hardened, well-armed guerilla fighters in unfamiliar desert terrain.
Foreign Minister Laurent Fabius said on Sunday that he thought involvement in the Mali campaign would essentially be aerial and claimed France's mission could be completed in a matter of weeks.