On Thursday, it was announced that Eubank would defend his British middleweight title against Tom Doran at London's O2 Arena on June 25, but the Brighton-based puncher already has his eyes on a clash with Golovkin.
Golovkin has added the WBC crown to his IBF and WBA titles after Saul Alvarez vacated the belt on Wednesday, and although the Mexican has maintained his interest in facing the Kazakh, Eubank is keen to become the next opponent for the hard-hitting fighter
The 26-year-old told Sky Sports News: "We want the big names as quickly as possible. There's no time to waste. I am 26 years old and these guys are there. I've always said that I want to fight the best in the world and I want to show the guys at the top of the division who's boss.
"Golovkin is considered as the best middleweight in the world and for me, he doesn't deserve that position. I feel like I have the tools to beat him so let's get it on."
Eubank has also been linked with a rematch with Billy Joe Saunders, who currently holds the WBO title.