Golovkin has been Alvarez's mandatory challenger since late in 2015, and the WBC said that negotiations must be completed by next Tuesday in order to set up a mega fight in September.
However, Alvarez has decided to give up his belt due to the time constraints put in place but the Mexican has signalled his intention to meet his pound-for-pound rival in the ring.
In an official statement, the 25-year-old said: "After much consideration, today I instructed my team at Golden Boy Promotions to continue negotiating a fight with Gennady 'GGG' Golovkin and to finalise a deal as quickly as possible. I also informed the WBC that I will vacate its title.
"For the entirety of my career, I have taken the fights that no-one wanted, because I fear no man. Never has that been more true than today. I will fight 'GGG,' and I will beat 'GGG', but I will not be forced into the ring by artificial deadlines.
"I am hopeful that by putting aside this ticking clock, the two teams can now negotiate this fight, and 'GGG' and I can get in the ring as soon as possible and give the fans the fight they want to see."