Diakhaby said that Cadiz defender Juan Cala directed a racial slur at him during the Andalusian side's 2-1 victory on Sunday, resulting in the game being suspended for 25 minutes. The Frenchman was substituted during the stoppage.
Spaniard Cala has denied racially abusing Diakhaby and said he had been caught up in "a media circus" and "a public lynching."
On Wednesday, radio show Tribuna Deportiva posted audio from the game on Twitter, in which they say the racist insult can be heard.
Diakhaby replied: "To not say anything is to be complicit," tagging La Liga in his Tweet.
Tebas, however, said the audio had been taken out of context and that La Liga is working on determining exactly what was said through the use of technology and an expert lip reader.
A report on the incident is expected to be published later on Thursday or Friday.
"There'll be more news either today or tomorrow. The audio in question is from a minute and a half after the incident, and whoever says it has a South American accent, so it can't be Cala," Tebas said.
"We've worked hard on determining this. It looks as if someone is saying to a group of players or the referee what they think has been said, but that recording isn't Cala.
"We've ordered the audio recordings from the game to be cleaned so we can see exactly what can be heard being said during the game.
"We've also employed a lip reading expert, too. Cala obviously says something, but we'll see what that exactly was. There'll be a report and things will be cleared up."