The experienced midfielder is no longer in the plans of Blues boss Roberto Di Matteo and has been ordered to train with the youth team.
Having entered the final year of his deal at Stamford Bridge, the 32-year-old is widely expected to leave the club in January.
L’Equipe claims that Malouda is likely to join Brazilian side Santos, who already attempted to sign the player in the summer.
The highly rated winger met with president Luis Alvaro Ribeiro in July, but his wage demands proved to be an obstacle to the deal.
However, Santos have since sold star player Ganso and are expected to reignite their interest in the Chelsea midfielder as soon as the transfer window reopens in January.
Florent Malouda has made a total of 149 Premier League appearances for the Blues, and scored 35 goals in the process.