The Mexican, 25, beat Khan with a thunderous right hand in round six to retain his WBC middleweight title.
Thoughts immediately turned to a unification match with Kazakh Golovkin, who holds the WBA and IBF belts.
"I will fight him at 160lb, no problem," said Alvarez, who fought Khan at a catch-weight of 155lb.
"Weight will not be an issue - we can even fight for no belts. I would have fought him in the ring tonight. I'm not afraid of anyone."
After his victory over Khan, Alvarez invited the watching Golovkin into the ring, although the rivals did not speak to each other.
The undefeated Golovkin, 34, has 32 knockouts from 35 wins and is the mandatory challenger for Alvarez's WBC title.
A fight between the pair is the biggest boxing has to offer and would be a boost for the sport following the anti-climactic fight between Floyd Mayweather and Manny Pacquiao last year and both boxers' subsequent retirements.
Alvarez won the vacant WBC title by outpointing Puerto Rico's Miguel Cotto at a catch-weight of 155lb last November, and it was thought weight would be a major sticking point when negotiating with Golovkin.
But after Alvarez's demolition of Khan, the Mexican's promoter Oscar de la Hoya said he would try to open talks with Golovkin's team the next day.
"Golovkin, make sure you answer your phone in the morning because we'll be calling," said De la Hoya.
"That's the fight the fans want and the fight Canelo wants. And those fans who were turned off by Mayweather-Pacquiao will fall in love with boxing again."
However, De la Hoya hinted at the tortuous negotiations ahead when he added: "There's no doubting who the star is. We have four aces and they have a pair of twos."
Saul 'Canelo' Alvarez says he is prepared to fight Gennady Golovkin at any weight after knocking out Britain's Amir Khan in Las Vegas.