The former Blancos striker says his compatriot has done well to secure a move to Spain but insists he must not be placed under pressure through comparisons
Chicharito joined Carlo Ancelotti's side on a season-long loan deal after being deemed surplus to requirements at Manchester United by Louis van Gaal.
Sanchez, who scored more than 200 goals in a seven-year spell at Santiago Bernabeu, is confident the striker will become a success at the club but insists he must not be put under pressure by comparisons with his own career.
"I'm convinced Chicharito will triumph at Real Madrid, as will Raul Jimenez at Atletico and [Javier] Aquino at Rayo Vallecano," he was quoted as saying by Record.
"If leaving Manchester United is difficult, he has done it to come to Madrid and that, of course, is commendable.
"Congratulations to Chicharito, hopefully he'll be lucky.
"I will not let them pressure him with comparisons. They are odious. I will not let them pressure Chicharito, or Raul, or Aquino.
"In my career, I had my own path; they will have theirs. What you have to do is support them, give them confidence, motivation and keep their confidence up."