Javier Barkero is believed to have accused his Granotes teammates of deliberately manipulating the outcome of the game in a dishonest fashion.
Mid-table Granotes lost 4-0 at home to relegation-threatened Deportivo on April 13, prompting some - including Levante midfielder Javier Barkero - to question the effort of some members of Juan Ignacio Martinez's men.
Barkero is believed to have confronted his teammates at half-time and alluded to their lack of commitment. Javier Tebas, president of the LFP - who has previously questioned the legality of a number of Liga fixtures - revealed he is optimistic about finally proving what he has long suspected.
"I will not go into any details because that would hurt our research. I was on the research process and I am convinced I will be able to prove it. There is considerable evidence and hopefully we'll come to a conclusion soon," he told reporters.
"The biggest hint is that there is a player who himself accused his peers, and that is very important to note. We are not just talking about fraud here, but also there's an issue of gambling."