Madrid will send a report to the European body's disciplinary committee on Thursday, according to sports daily Marca, which added that the Spanish club considered Tuesday's actions "an intolerable provocation."
Van Bommel, a former player with Madrid's archrival FC Barcelona, volleyed Bayern's late second goal in a 3-2 defeat at Madrid's Santiago Bernabeu Stadium.
The 29-year-old midfielder apologized, but said he had been insulted by a Madrid player about his Barcelona connections. He didn't name the player.
"It's the first time I've played at the Santiago Bernabeu and I have nothing against the crowd although I do have something against a player," he told Catalunya Radio.
Marca reacted with indignation to the incident, with its front page accompanying a photo of Van Bommel gesturing with the headline: "They're going to have to swallow this."
The paper advised Madrid players to "cut the photo out, stick it in the dressing room and don't stop looking at it until the return leg."
Sports daily As added that Madrid will also protest that Bayern substitute Hasan Salihamidzic spat at supporters behind the goal straight after Van Bommel's goal, reports AP.
Madrid left-back Roberto Carlos said Van Bommel and Salihamidzic's actions were "disgraceful" and "do soccer no good."
"The best moment of the game is when you score. If you gesticulate or insult people it shows a disgraceful lack of respect," the Brazilian was quoted as saying by Marca's Web site.
Van Bommel joined Bayern last August after a year with Barcelona, in which he helped the Catalan team win the Champions League and Spanish title.
Bayern and Madrid meet again in Munich on March 7.