Disciplinary proceedings have been opened against their duo for their conduct during the Champions League final, while both Madrid clubs could also face sanctions
Simeone was embroiled in a heated confrontation with Real Madrid players and the referee after becoming incensed when Raphael Varane kicked the ball into the dugout during extra time.
Alonso, who was watching the game from the stands after being suspended for the clash in Lisbon, could face similar misconduct charges after he ran down the touchline to celebrate with team-mates after Bale's header.
Both Atletico Madrid and Real also face sanctions each side received more than five yellow cards during the match, while Uefa has also taken exception due to the conduct of supporters in Estadio da Luz, with fireworks set off from both sections of fans.
Uefa's Control and Disciplinary Board is set to meet over each of the incidents on July 17 before confirming whether action will be taken.
Madrid claimed their 10th European title in the clash on May 24 as goals from Sergio Ramos, Bale, Marcelo and Cristiano Ronaldo secured a 4-1 win after Diego Godin's opener.