GGG overcame a slow start on the weekend to overcome Ryota Murata in Japan to unify the middleweight division. Golovkin now holds the WBA, IBF and IBO titles at 160lbs.
Golovkin is now in line to challenge Canelo - who takes on Dmitry Bivol at light heavyweight in May - for the undisputed title in September on Mexican Independence Weekend.
The two rivals have fought twice - the first in 2017 and the rematch being the following year.
In 2017, GGG was robbed of victory while the second encounter was a razor-thin win for Canelo.
Golovkin took a lot of punishment from Murata in the first couple of rounds but he eventually stopped the Japanese Olympian in round nine.
At 40, Bradley does not see Golovkin having a chance of beating Canelo should they collide in a trilogy contest later this year.
"He's going to mop up Golovkin. I thought Golovkin looked terrible at the beginning and then closed strong at the end, which is good. It showed that he has great conditioning. He's still able to fight," Bradley told Fight Hype.
"He still has some power, yeah. Punch placement, and I saw some good lateral movement from him. But Canelo is on another level, man, for Golovkin."
"[Going to 168], that's going to slow [Golovkin] down, I think that's honestly going to slow him down. It's a different animal [with Canelo]. It's [Golovkin's] first fight at 168 pounds. Canelo has fought at that weight and 175.
"Come on, dog. So, I see [Canelo] beating him and stopping him late. You saw it early on in his fight against Murata, Murata was going down to the body and pushing him back. That's what Canelo is going to do. He's going to press forward [against Golovkin].
"He's a little more slippier than, a lot more slippier than Murata and he's going to be landing his kill shots over the top, right hands, left hooks, whatever. He's going to set him up.
"I think conditioning-wise, Canelo is at his peak right now, he's fighting at his peak. I see him stopping [Golovkin], bro, and if he doesn't stop him, he's going to hurt him really badly in the later rounds for sure."