The website of Dutch-language Belgian daily Het Laatste Nieuws said that "just before the accident, the driver wanted to put a DVD" in the player.
The newspaper, without directly identifying the sources, said "this is what injured children told their parents and medics" in Swiss hospitals.
The daily reported from Switzerland that a teacher with the schoolchildren had taken a DVD to the driver shortly before Tuesday night's crash in an alpine tunnel.
The paper said that a "moment of distraction" could have led to "the driver losing control."
A Swiss police official, Renato Kalbermatten, told the newspaper this was speculation, saying there was no confirmation available via the crash tunnel's closed-circuit cameras.
Swiss daily Aargauer Zeitung reported the same claims.
Swiss officials said the body of the driver was expected to remain in the country after the rest of the dead are repatriated to Belgium and the Netherlands.
Officials said "health analyses have to be carried out" to check if he was suffering from an illness that could have caused the accident.