The Mexican great, 31, dominated American star Caleb Plant in November to become the first ever undisputed super-middleweight champion in the history of boxing.
Congolese southpaw Makabu, who was once beaten by Tony Bellew, hasn’t fought for well over a year.
But Thurman says he can’t really see what the problem is as he believes he has merely copied Mayweather’s strategy for maximising his career for the ultimate gain.
When asked by Fight Hub TV if Canelo has cherry-picked his opponents, he replied: “Yeah, but so what? He’s Canelo!
“The people love him. He’s got a huge following. He’s brought tons of excitement.
“You can say he’s cherry-picked a little bit but he’s kinda [sic] learned from the best. He got beat by Floyd and now he’s starting to make money like Floyd.
“Are there greater challenges out there for Canelo Alvarez? Most definitely.
“Are there fights that I would truly love to see? Most definitely.
“Are there super talented individuals that might be able to give him problems? Definitely.
“But does he have to do any of those things? Absolutely not.
“Whatever he wants to do, what he likes to do, what makes him want to get out of bed and excited and elevate himself and his career, that’s what he’s going to do.”
And while he can understand the criticism, Thurman argues Canelo has earned the right to fight whoever he wants.
He added: “There’s many different styles that he’s yet to face that I believe are some of the most exciting fights in that division that could manifest.
“But just because of his status and his stardom he gets to entertain the world in the way he chooses fit, and at a certain degree you just have to respect that, because it takes a lot of hard work and effort to build yourself up to get to that level.
“So when a fighter finally achieves that level and that status and they want to hold onto it and manipulate the industry a little bit, to me you can be mad, you can be sad, but you’ve got to put some respect on the game too.”