Golovkin, who was making his Las Vegas debut, and Alvarez fought to a draw on Saturday in a evenly-matched bout that lived up to its hype as a showdown between the top two middleweights in the world.
Both the 27-year-old challenger Alavarez (49-1-1, 34 KOs) and the 35-year-old Golovkin (37-0-1, 33 KOs) said they wanted a rematch.
"It seemed like everyone came away from that fight with an unsatisfied feeling," Tom Loeffler, of K2 Promotions which oversees Golovkin's fights, told the Los Angeles Daily News.
Golovkin and Alvarez now look set to rule the resurgent middleweight division for years after their slugfest ended in a stalemate.
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Judge Don Trella had it 114-114 while Dave Moretti scored it 115-113 in favour of Golovkin of Kazakhstan.
Golovkin got his first taste of Nevada-style judging in his Sin City debut, when the third judge, Adalaid Byrd, scored the nail-biter 118-110 in favour of Alvarez.