The captain of the plane, Rustern Salikhov, received his certification from one of the centers licensed by the aviation watchdog Rosaviatsia, RIA Novosti reported.
"Investigators have raised doubts over the legality of the activities of these centers, which have since closed down," Vladimir Markin, spokesman for Russia's Investigative Committee, said.
Markin said investigators would search for paperwork related to the training centers and question people who headed departments at them.
Salikhov was an experienced pilot and had 2,500 hours of flight time, Tatarstan Airlines said after the Boeing 737-500 crash on Nov. 17.
The pilot was attempting to land at Kazan Airport when the plane overshot the landing and crashed.