Hercules coach Quique Hernandez has accused the then-Sabadell defender Abraham Paz of "selling himself" during the game on March 17, which Hercules won 3-1.
Paz, who has since left the Catalan side to join Israeli club Bnei Sakhnin, strenuously denies the allegations.
"Recorded conversations have come to light and the league is aware of them," Javier Tebas told AS.com while on a promotional visit to Buenos Aires.
"The Sabadell coach, Mr [Lluis] Carreras, informed the league about the conversations, and we have informed the police and filed a complaint to the Spanish Football Federation.
"The conversations took place in May, the Federation and the police know about it and it will be subject to legal process."
Tebas was elected as LFP president in April and has made cleaning up match-fixing his number one priority.
He again pledged to act tough on any teams involved in the practice.
"We want a clean sport and so sanctions should be put in place, such as automatic relegation or points deduction," he said. "Our sport and our competition must be clean.
"The worst thing would be to know about these things and not denounce them. We must have an image of promoting clean sport.
"I have to recognise that up until now this subject has been treated as a minority issue."