Alvarez retained his WBC middleweight title thanks to a sixth-round knockout of Amir Khan in Las Vegas on Saturday.
The 25-year-old already has his sights on his next fight – and it is Kazakh Golovkin, also a middleweight champion, that he wants.
"Like I said in Mexico, we don't f*** around," Alvarez said through a translator.
"We don't come to play in this sport. I fear no one in this sport. I'll fight him right now. Let's put the gloves on and get in there with him."
Khan, fighting above welterweight for the first time, troubled Alvarez with his speed early in their bout.
However, Alvarez landed the big blow in the sixth round with a huge and frightening right hand.
Alvarez said: "Many people focus on my power and talk to my power but I have many more qualities in the ring.
"I like to surprise everyone."