Well, maybe to start, I will ask you to read an article I wrote on this topic in
Yoga International. In it, you will see there are several things can will affect how deep one can go into squat.
The real question is "what is stopping YOU?" Where do you feel resistance? In the ankles, the back of the knees, the front of the hips? What you will need to work on will depend on the answers to these questions.
There are similar postures to squat which may give you some clues. For example: Child's Pose is basically squatting on your belly, without the need for any ankle flexion. Can you easily have your chest on your thighs and legs together in Child's Pose? If so, your restrictions are not the knees or hips, so then we would look at the ankles. However, if you can't get your buttocks to your heels, maybe knee flexion is stopping you. In that case, squatting wont be great for you because it does require a lot of flexion at the knee. If you can get butt to heels, but can't keep your legs together, maybe hip flexion is your restraint. In that case, do your squatting with knees and/or feet apart! That is not a crime and is allowed.
Let's assume Child's Pose is child's play for you, then we think of the ankles. How far in front of your toes can your knees go? Try the "overstepping Dragon" position to test this: basically this is a low lunge with the knee coming far in front of the front foot (bring the back leg up close so that you are not stopped by tightness in the quads, and if you feel stuck at the hips, point the front knee and foot outward.) Getting into squat will require that the knees can come some 15~20 cm in front of the toes (that's about 8 inches or so.) Some people can't do that, so the question for them is - why not? What's stopping them? The answers are either tension in the back of the calfs or compression in the front of the ankles. Tension can be reduced overtime, usually by doing poses just like this one. Compression however is final. You won't change that.
If you are stopped by compression, then squatting will require you to lift your heels. This is also not a crime! To stay there, place blocks or folded blankets under the heels. Now you can relax.
For some people, however, squatting actually is quite accessible, but what stops them is getting into squat, not the squat position itself. Maybe this is you? If so, try this: start on the floor! Bend your knees, bring your feet towards you and lift up into squat. Did that make it better?
Good luck!
Cheers
Bernie