Simeone's side claimed the trophy with a 1-0 win on the night, but the Argentine was sent to the stands in the first period for arguing with the officials.
According to Marca, the LFP could also punish the former Atletico midfielder for watching the match from behind the dugout rather than heading higher.
Article 114 of their disciplinary code states: "Anyone sent off, whether they are a player or a coach, must head straight to the dressing room and may not watch the match from the stands. A failure to do so is punishable with a suspension of one to three games."
It is understood that the ban could start in time for Atletico's league opener against Rayo Vallecano on Monday.