Eubank Jr. has demanded a fight with the Pound for Pound superstar, who is yet to name his next opponent. The second-generation fighting Eubank currently holds the WBA interim title at middleweight, with Canelo being the titleholder of the WBA full version of the belt.
Canelo is also the WBA "regular" super middleweight champion and in his last bout, he defeated Sergey Kovalev to become a four-division world champion at light heavyweight - just the second Mexican to win world honours at 175-pounds.
Canelo will face Anvi Yildirim next, a former opponent Eubank beat, while the Englishman is in line to challenge for the WBA title at middleweight.
"I personally would like to fight Canelo," said Eubank to the BBC. "The fight has to happen. It's one so many fight fans are calling for. I'm number one contender so he needs to fight me or give up that belt.
"I wouldn't say I'm unfulfilled. I've had a great career, made a name for myself in the sport and I'm financially stable for the rest of my life. But is there more I can achieve? Absolutely. And I will achieve those things."
Eubank links up with Roy Jones Jr.
During the coronavirus pandemic, Eubank has appointed boxing legend and former four-division world champion Roy Jones Jr. as his trainer.
The American - who returned to the ring in 2020 to face Mike Tyson in an exhibition fight - has been credited with improving Eubank's boxing IQ.
"At this stage of my career I don't think it's possible to completely change a fighter but I have this renewed energy now with Roy that I didn't think was possible," said Eubank.
"Now I'm excited about what am I going to learn. I've never really had this relationship with anyone in boxing. I have learned a hell of a lot from my father but he hasn't been able to be there day in, day out like a real trainer needs to be. This time and moment in history has been a blessing to me.
"No disrespect to anyone affected negatively by Covid-19. If it hadn't have happened I wouldn't be where I am now."