My legs are disproportionately large, and this has been the case since my childhood due to genetics. This is what is known as the t-rex (opposite of chicken legs). Is there a way I can keep training, namely keep doing squats, and reduce the size of these muscles?
I think we all have genetic predispositions when it comes muscles. I find it very difficult to build up my chest, but have no problem building muscle in other areas.
If would continue squatting and performing other lower body exercises, I would cut back on the volume quite a bit and maintain the intensity (weight/tension). Not knowing what your current program consists of, it is difficult for me to give you any specific paramaters. The other possibility is to perform lower body exercises with bodyweight only. Without the excess tension, you should see some atrophy.
The next thing you want to do is add volume and intensity to your upper body workouts. Perform compound movements, namely bench presses, overhead presses, dips, chins, rows, etc. For every lower body exercise you perform, perform 2 or 3 upper body exercises. The quickest way to make your legs looks smaller, is to make your upper body look bigger. Hopefully that will bring you some semblance of symmetry.
Go for maximal strength workouts. Those develop strength rather than mass.
And, follow these other nine steps in the link below. Sorry for linking a "men's fitness" page but the principles are very sound nevertheless :)
There might be a way to reduce the size of your legs, but I don't know what it is. Instead, I'd recommend A) not worrying about it and B) making your upper body enormously muscular and awesome, to reduce disproportion.
For instance, maybe only do squats and deadlifts every other workout, while continuing to do upper-body work? So, every workout involves multiple upper-body exercises but only half the workouts involve lower-body exercises and even then those exercises are a small portion of the workout.
I might also move away from squats and focus more on deadlifts. (This would only help if your problem is exclusively quads and thighs rather than hips, thighs, and buttocks.)