Callejon re-signed for Madrid in the summer in a €5.5 million deal just three years after leaving the club.
The winger, who came on as a substitute in Madrid's 6-0 win over Zaragoza in the opening round of La Liga fixtures, hopes to make a bigger impression at the Spanish giants than some other talented players who have come before him but failed.
"I do not want what happened to Pedro Leon and Sergio Canales to happen to me, though I am aware that on this team only the best play and that it will be hard to play, but I trust my chances," Callejon said at a press conference.
"The atmosphere, the fans, the quality of the players I train with every day and the coach, a great person with a lot of joy both on and off the pitch, everything is great."
The 24-year-old has agreed a five-year contact with Madrid, where he came up through the youth ranks before moving to Espanyol in 2008 without making a first-team appearance for the Bernabeu outfit.