There are several web sites run by CPS that all, typically have different info about the Magnet/Option programs. They are allegedly coordinated according to both age/ class AND type of program but, despite being up and running for DECADES there is horrible coordination.
There are also allegedly deadlines after which applications are not allowed, but "knowing somebody who knows somebody" routinely result in these rules being bent.
I suggest seeking out someone whose child is just a bit older than yours and has been successful in the CPS. They don't make it easy to transfer into the system, but there are some who have been successful.
Realize too, that by "bending the rules" you may end up in classroom with WAY MORE kids than are supposed to be enrolled. If you are happy, you student, and the teacher does not mind, you'd think no problem. Of course if that school's Union Rep. knows the right people your child could be reassigned so that the rules are not violated. It happens.
It is a crazy system that has lots of broken parts. A lot of talent is wasted. Many parents grow frustrated and send their kids to private schools at great expense. The kids that get good education even in the best magnet elementary/middle schools are the exception. Those that go on to the very selective magnet high schools CAN get a fabulous education, but they have to jump through a ton of hoops, and endure a huge amount of dysfunction.
CPS Magnet Program