According to Spanish outlet Marca, the strained relationship between Valverde and Tchouameni escalated after a hard tackle in training earlier this week.
The conflict is said to have escalated after another tackle in training by Valverde the following day.
Tchouameni then sought out Valverde in the locker room, and what was initially described as a heated exchange of words is said to have turned into a fight.
The incident ended with Valverde being taken to hospital after hitting his head. According to French outlet RMC, the midfielder was unconscious for a few seconds.
The club states that information regarding possible measures will be provided once the internal investigation is completed.
