C.C.
Although Lexxa is right that the mom can choose to sign over guardianship to you, it would be complicated, and you would definitely need to involve a lawyer if this were even possible.
I recently adopted the most beautiful boy from the foster care system. First, I would say that you should call HRT. I think that stands for Human Resource something or other. (Look them up on the net!) They certify people for foster care and/or adoption for free if you are going through AZ's DES. They may be able to put you in touch with his caseworker at DES (since they have connections), who could make it happen for you. But if you really want this you are going to have to be the squeaky wheel to make sure you get noticed!
Just so you are aware, AZ does reunite about 80% or better of kids with their parents. The time between when the child is placed in the foster care system and when parental rights are severed varies. In my son's case, his mom was given 2 years to correct the situation (even though she was completely unresponsive to any attempts to work with her). However, if you want to go through with this you need to make some contacts SOON and move forward. The sooner the better! Once the parental rights are severed, DES will hold a "red file staffing", which is when they take all the options and decide who the adoptive parents should be.
If he is currently in the foster system, the case worker would be able to transfer him to your care until the rights were severed once you are certified as foster parents, but only if the case worker felt it was in his best interest. Also, the longer he is with another family, the less likely it is that you would be able to get him with you unless the other family were to choose not to adopt once the parental rights were severed.
Feel free to email me with any other questions. I know this is a lot to take in, but if you are proactive, you can make this happen! Good luck!