Conte was widely-tipped to replace Julen Lopetegui at the Bernabeu after a dreadful run of games for Los Blancos.
But according to Spanish TV channel Cuatro, the former Chelsea boss feared he would not be welcomed by the players.
The report said: "Conte has made the decision after giving it a lot of thought.
"The reasons for the breakdown in the negotiations are unknown, but they are not thought to be financial.
"It may be that Conte felt that not everyone in the dressing room would be in favour of his arrival."
The reports come just 24 hours after Sergio Ramos' comments at the Nou Camp suggesting a potential new manager needs to make a good impression if Lopetegui is indeed replaced.
Ramos said: "Respect is earned, it is not imposed. Neither a name nor another.
"We have won everything with coaches that you already know, in the end the management of the players is more important than the technical knowledge of a coach."
After the 5-1 El Clasico humiliation yesterday to leave Los Blancos NINTH in LaLiga, Lopetegui is on the brink of losing his job.
The Real Madrid board are meeting this afternoon to discuss the former Spanish national team coach's future.
And many expect for him to be sacked before his side travel to Melilla in the Copa del Rey on Wednesday evening.
It means Santiago Solari is now the favourite to take over instead.
The coach of Real Madrid Castilla, the club's B team, has impressed during his time in charge and could come in on an interim basis.
Lopetegui reportedly said his goodbyes to the players after the game last night but stunned them by turning up and taking training this morning.
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