The News of the World says Anelka signed a new four-year deal at Bolton in the summer despite being linked with a move away from the Reebok Stadium.
But the contract is widely believed to include a £10m get-out clause.
And with Bolton in disarray, both on and off the pitch, the departure of Anelka seems inevitable.
City have had problems up front where £8.8m capture Rolando Bianchi has struggled and Belgian Emile M'Penza has been preferred on occasions.
But neither look a prolific scorer which is why the clinical-finishing Anelka will be a transfer-window target on January 1.