Just my own personal theory, but I think Negan views Carl as a potential protege. There doesn't seem to be any children in the right age range around him (old enough to understand yet still impressionable), and even fewer with the experiences that Carl has gone through, dealing with the world as it is now. I think he sees the potential to slowly manipulate Carl, turning him to the dark side (oh crap...now I'm off track
). Who knows if Carl can be converted or not, but I think Negan is going to try. In the end, Negan's ego is so big that I'm sure he wants a successor to his empire after he dies, otherwise it will be all for naught in his eyes.
Carl is now a bit of a disgruntled teen with black and white views on the world and a penchant for aggressiveness and violence. It's just the sort of kid who Negan can mould to fit in his world.