Filin suffered burns to his face and eyes when a masked man threw sulfuric acid at him outside his apartment Jan. 17.
Citing a source it did not identify, the newspaper said Tuesday police had detained Pavel Dmitrichenko, a Bolshoi dancer since 2002. Police confirmed investigators searched Dmitrichenko's home and had detained another suspect.
The source told the newspaper Dmitrichenko was in a relationship with Angelina Vorontsova, a Bolshoi dancer who was a protege of Nikolai Tsiskaridze -- described as a rival of Filin for artistic control of the Bolshoi.
The source said Tsiskaridze "inspired" the attack on Filin but did not order it.
Izvestia identified the second suspect as Andrei Lipatov, and said he allegedly drove an accomplice, Yury Zaretsky, to Filin's home, where the attack occurred.
Interfax said police were searching for Zaretsky.
Filin has undergone several surgical procedures to save his eyesight and is receiving follow-up treatment at a clinic in Germany, The New York Times reported. An unknown individual or individuals had harassed Filin by phone and email for weeks leading up to the attack, the newspaper said.
Citing news reports, The Moscow Times said police used telephone records to identify Lipatov and Zaretsky as suspects in the attack on Filin.