The Sun says the pair have been banished from first-team training by Villas-Boas.
The duo are no longer in the Chelsea manager's plans and it is understood Brazilian centre-back Alex has put in a transfer request.
Anelka is expected to head to Russia in January and join Anzhi Machakala.
But the rest of the Chelsea squad have been shocked at the manner in which the popular pair have been cast aside.
Both are now training with the reserves.