Andy Ruiz on Anthony Joshua Rematch, I've Got Some Demands!

Heavyweight boxing champ Andy Ruiz says he's already training for the rematch with Anthony Joshua ... and tells TMZ Sports he's calling the shots this time around!!

Of course, Ruiz was a late replacement who stepped in for Jarrell Miller when "Big Baby" failed a drug test -- with Andy only getting around 6 weeks of training before the June 1 fight. 

But this time around, Ruiz tells us he's working in a FULL training camp -- and he's going to be the one to decide WHERE the fight takes place. 

Ruiz tells us he'd like to throw down in Mexico -- where he recently met with President Lopez -- or go back to Madison Square Garden in NY. 

There's one place he won't go ... England, where Joshua is from. 

Bottom line ... "I'm the champion," Ruiz says -- "We're the A-Side."

As for whether he's spoken with Joshua, Ruiz tells us, "I haven't talked to him, but I'm pretty sure he's training hard for the rematch. And, so am I."