Hmm, it may be a bug because it should be there. What do they say when you click on them? There's two separate drawers, top and bottom.
The top one says "The drawer is filled with towels and washcloths" and bottom says "There's various cosmetics and toiletries inside the drawer"
Let me try saving and restarting game - I have had the game open since I initially started playing and its possible something broke?
I got it after restarting the game! Seems like there's some minor bug that kept me from doing it before though.