Alvarez needed only three rounds to see off WBC mandatory challenger Yilidrim in Miami, defending his WBC and WBA titles.
Within hours of the win a bout with WBO champion Saunders was confirmed for May 8 in a venue to be determined.
"We want to unify the division," Alvarez said. "He's a world champion, we want to go for it and we need to go for it. He's a very difficult fighter and has a championship, the WBO.
"People talk but I'm a very mature fighter and I know how to control myself. All I need to do is go into the ring, win and make history."
"It's because it hasn't been done, no one has done it in Latin America. In the world only a few fighters have done it, the best. I want to make history and be one of the best in the world."
Saunders, who boasts a 30-0 record, will be defending his title for a third time after most recently sending Martin Murray into retirement with a comprehensive win.
"Canelo, I'm ready to rock and roll," the 31-year-old said. "You have to dare to be great and you aren't going to be a great if you don't beat the greats.
"I believe I am the only one with the footwork, knowhow, skillset, mindset and brain to unlock that door in Canelo.
"He's the main man in the sport and the face of boxing. You have to give him respect, he hasn't ducked anyone, he's beaten good names, but nobody is unbeatable, and I believe I have got the tools to beat him if I use them properly and if the gameplan comes off that I believe works."
Alvarez made light work of Yildirim in Miami, securing victory when the Turk retired late in the third round.
Alvarez had a strong start as he hit Yildirim with a big left hook then spent the remainder of the first round working the Turk's body.
Yildirim copped more shots in the second as Canelo continued the punishment, with the challenger knocked down by a straight right in the third.
Yildirim got up but his corner waved the fight off moments later, marking the third loss in the Turk's 24-fight career.