Cagliari said Trepy "is currently in intensive care at the hospital in Sassari," adding the club remains "in close contact with the medical staff and the player's family".
"The club asks for privacy to be respected and will provide further updates as soon as possible," Cagliari said in a statement without disclosing the circumstances of the accident.
Italian media reported Trepy had to be rescued after swallowing a lot of water in a swimming pool on Sunday in Porto Cervo, northern Sardinia.
He was placed in a medically induced coma, the reports added.