The referee did not mention the chants in his report on Real's La Liga game at home to Celta Vigo on Saturday but Javier Tebas, the LFP president, said the league would report the fans to the Spanish federation's (RFEF) competition committee.
Clubs, football authorities and the government have pledged to crack down on violent and abusive fans known as "ultras" after a Deportivo La Coruna supporter was killed in apparently organised fighting near Atletico Madrid's stadium late last month.
"Our qualitative step forward or new commitment is that if the referee does not hear it we will draw attention to it," Tebas told Spanish radio station Cadena Ser.
"There were insults and unacceptable chants at the Bernabeu, so I gave the order to report them," he added.
Real, who along with Barca and Espanyol are among the few clubs who have tried to banish ultras from their stadium, were not immediately available to comment.
The European champions had identified 17 fans who took part in the abusive chanting, which also targeted the region of Catalonia, and they had been banned for life, local media reported.
Several other matches, including Atletico's game at Elche, Malaga's at Deportivo and Rayo Vallecano's at home to Sevilla may also come under scrutiny, they added.
Real coach Carlo Ancelotti called for an end to abuse in stadiums when asked about the incidents on Monday.
"We all have to understand that an insult is a violence for everyone," Ancelotti told a news conference.
"I would like supporters who back us the whole match singing for the team and the club and nothing else," added the Italian.
Tebas said more should have been done sooner to banish ultras from stadiums and their surroundings.
"I made a mistake in not seeing this as a problem in football and I won't make it again," he told Cadena Ser.
"We have fattened up a monster which must be banished. We have taken this decision and we will continue down the same path."
(Reporting by Iain Rogers; Editing by John O'Brien and Ken Ferris)
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