Manuel Pellegrini faces the sack if Real Madrid are beaten by Getafe on the weekend.
Sport says the ultimatum came just hours after Real's Copa del Rey humiliation by Alcorcon.
The decision to dismiss Pellegrini would hit Real's finances hard. The Chilean is on a two-year deal at Real and would be due a massive €11 million in compensation - the equivalent of Cristiano Ronaldo's salary.
Three losses, one draw and a win in the last five games is enough for Pellegrini's position to be questioned, however it was the manner of their Copa defeat which has most angered Real's board.
Even victory over Getafe may not be enough should Real lose to Champions League opponents AC Milan in Italy next week.