I don’t think this is supported by wordpress out of the box. What you can do is have the categories as menu items, and when you click on them it takes you to a page that shows all the posts of one category. But I don’t think this is what you want.

Alternatively there are premium menu plugins like ubermenu3 that allow for this type of behaviour. Ubermenu for example allows you to place widget areas aas dropdown, in which you can have a listing of all the posts in a certain category (using widgets).

I hope this helped a bit, let me know if I can be of further assistance.