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The club believe that adding Madrid to the name would make the club more attractive to sponsors.
Granada have dismissed coach Paco Jemez after the club's worst start to a season since the 1944-45 campaign.
Atletico Madrid midfielder Augusto Fernandez has promised to come back strong after having surgery on a torn anterior cruciate ligament.
"If Araujo is found to have been negligent, we will open disciplinary proceedings for that but we are not going to hang him in the town square.
Real Madrid coach Zinedine Zidane said he felt "screwed" after his team conceded a late equaliser in Tuesday's thrilling 2-2 Champions League draw.
Francesco Totti has revealed further details about how close he actually was to joining Real Madrid in 2003.