Detectives from Hermosa Beach are expected to complete their inquiries into the circumstances surrounding Cousins' admission to a Los Angeles hospital following a suspected cocaine overdose.
If charges are laid, it would dent the exiled Eagle's hopes of avoiding punishment at an extraordinary AFL commission meeting in Melbourne on Monday.
The 29-year-old's spirits have soared in recent days after West Australian police were forced, on a technicality, to withdraw a second criminal charge laid against him following his dramatic arrest in Perth last month.