Your second sentence sounds much better.
Many native speakers might say the first sentence, but it is not correct. Change "if" to "whether" to make it correct. It does sound natural but in most cases the second sentence sounds better and more businesslike.
Also, I am not sure whether "director" is the person you mean here. It might be, but for most people it would be their immediate superior, immediate supervisor, or immediate manager.
In a company that has more than one director only a very few employees would be immediately reporting to them. Most would report to an intermediate manager. In that case it may still be your director's decision whether or not to promote you, but s/he would not be your immediate director.
I am from the UK, so things might be different in the US, or any of the other English speaking countries.