"he has almost nothing" or "he hasn't almost anything"?

Hasn't almost anything sounds wrong in many ways. 1) Hasn't can't be used here because has is denoting possession of something. 2) Almost anything doesn't seem right because you're using it in a negative sense. 3) Even if you don't use the contraction hasn't, it's not right. Because, you can't say "has not anything", it should be "has nothing". But "He has almost nothing to eat in his cupboards" is perfectly fine.