Jose Mourinho and Cristiano Ronaldo have been given two-match bans following the Copa Del Rey final on Friday.
Mourinho was sent to the stands for remonstrating with the officials during Real's defeat to rivals Atletico, while Ronaldo was dismissed for aiming a kick at Atletico captain Gabi late in the game.
With Mourinho reported to be making the switch to Chelsea in the close season, his suspension could be honoured in England, should the FA deem this necessary.
Meanwhile, Ronaldo - who has also been linked with a move away from the Bernabeu - stands to miss the first two games of next season's La Liga campaign.
Mourinho's departure from Madrid was confirmed on Monday after the club finished the season without a trophy.