League spokesman Juan Carlos Santamaria said Friday the league is examining Deportivo's 4-0 win at Levante on April 13.
Levante issued a statement on its website saying it will "help and collaborate with any investigation."
"I have spoken with (league president) Javier Tebas and he has passed on indications (of a fix)" Levante club president Quico Catalan told El Pais newspaper.
Deportivo coach Fernandez Vazquez denied any wrongdoing by his club.
Following the heavy loss to Deportivo, Levante forward Jose Barkero apparently accused four of his teammates— captain Sergio Ballesteros, goalkeeper Gustavo Munua, forward Juan Luis "Juanlu" Gomez, and defender Juan Francisco "Juanfran" Garcia— of a suspicious lack of effort in the match.
Barkero later publicly retracted his accusations. It is not clear if the league had already begun investigating prior to leaks of Barkero's accusations.
"I only want to make public what I have told my teammates," Barkero said at a news conference on Wednesday. "I asked them for forgiveness, above all my four teammates, those who I accused of something erroneous. I ask Ballesteros, Munua, Juanlu, and Juanfran for forgiveness for what I have done to their image, their persons and their family, because they didn't deserve it.
"I am the one who was wrong. I accused them of something that didn't really happen."
Match-fixing is a crime in Spain and can lead to prison time for individuals or expulsion of a club from official competition.
Deportivo is in a fight to avoid relegation. Stuck in last place in Spain's first division last month, it started a four-game winning streak that ended with the lopsided victory at Levante. The previous wins were against teams also struggling to avoid relegation—3-1 over Celta Vigo, 3-2 over Mallorca, and 3-2 over Real Zaragoza.
Deportivo has since tied two more games and currently lies one point above the relegation zone with five games left.
"As an athlete I'm slightly offended," Vazquez, the Deportivo coach, said. "But I believe that we athletes have our conscience clean. I don't know about Barkero."
Deportivo became the latest Spanish club to seek bankruptcy in January. It spent last season in the second division and would take a hard economic hit if it dropped down again this summer.
Levante, meanwhile, has lost four straight games, its worst run in two seasons under coach Juan Ignacio Martinez. The modest Valencia-based club was the darling of the Spanish league last season when it briefly occupied first place in the standings for the first time and ended the season by qualifying for the Europa League.
Tebas, who was recently elected league president, said that one of the priorities was stamping out match-fixing.
"UEFA and FIFA say it only happens in 1 percent of matches," Tebas told El Pais on April 28. "But if one game of the 380 played in the first and second division is fixed, it's a serious problem. The first thing we have to do is recognize it's a problem. "