To be close to someone, he or she has to know you. For you to be known, you're going to have to reveal yourself, divulge yourself. What do you want? What do you like? What makes you angry? What scares you?
To whatever degree you don't share these truths about yourself, to that degree you are not known, and to that degree you will feel distant rather than close.
Find out more: How to Cultivate Closeness.