The former Mexico international says that the Cote d'Ivoire striker would be a big hit at the Santiago Bernabeu, while adding that he hopes Jose Mourinho stays at the club.
The Ivorian forward scored the winning goal in Chelsea's 1-0 Champions League triumph over Barcelona on Wednesday, and Sanchez admitted that he has been a fan of the African for some time now.
"One of the strikers that I wanted to see at Madrid is Drogba," he told Goal.com. "I said the same thing about Ruud van Nistelrooy, and I recommended Drogba years ago.
"The thing is that too much time has passed now for him to join Madrid. No one paid attention to what I said. But Drogba has long been one of my favorite strikers in the world, and he had an amazing match against Barca yesterday."
Looking ahead to Saturday's Clasico at Camp Nou, the 53-year-old believes that Madrid will look to attack due to the four-point advantage over Barca in the Liga table.
"Madrid will need to be aggressive," Sanchez noted. "The difference in points will allow them to take some risks. If you give Barca enough space, it is very hard to beat them. Only a few teams can beat them at Camp Nou, but Madrid are one of them. They have to go out to win, because that is all that they can do.
"Last season, Jose Mourinho's strategy in some matches was not the correct one, and when you play at home, you always have to be brave and try to win. I hope he will get it right, just like he did in the Copa del Rey final."
The Portuguese coach has been coy over his long-term future at Madrid, but Sanchez has indicated that he does not want to see the former Inter boss leave anytime soon.
"I would like him to stay because he is doing very good things at the club," he added. "I have agreed with him in many of the things he has said and done. In other cases, I would not have said or done the same thing, but I understand why he is like that.
"Mourinho is very clever, I really like his intelligence because I am a bit like him as a coach."
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