There is no contracted form for "am I not" hence, "aren't I" is used instead.
However, you can use "I'm late, am I not?" and it will still be correct. This is simply the complete way of phrasing it.
It is the same for other pronouns:
He is late, isn't he. → He is late, is he not?
You are late, aren't you. → You are late, are you not?
Only in using the contracted form for "am I not" will "aren't I" be used instead. Note that the correct way of phrasing it is "am I not" and not "am not i".
☺ Hope this helped.