Yes, it’s normal to have daily 'sleep' in your eyes — as long as it's not a lot. If you notice more or it has a very sticky texture, to the point that you struggle to open your eyes, that is a sign that something isn’t right.Yes, it’s normal to have daily 'sleep' in your eyes — as long as it's not a lot. If you notice more or it has a very sticky texture, to the point that you struggle to open your eyes, that is a sign that something isn’t right.