well, the manga doesn't say anything about her, but who doesn't want him to finally see the light and wake up from that oblivious goal of his that he'll get with kagome? (although him and inuyasha fighting is really hilarious)

Ayame is an anime-only character, so the manga didn't address this at all. We'll have to wait for the continuation/ending of the anime to see if they'll tell us what happens between those two! I hope Kouga sees the light and gets with her, though. :)

He should, it is the better choice for him.