As Draco had a high disgust for Muggle-Borns when he grew up, he treated Hermione with disdain. Hermione's friends and herself shared a strong enmity to Draco from virtually the moment they met, and her beating Draco in school marks, for which his father berated him. From time to time, Draco would call Hermione a mud-blood which usually set off the temper of her friends and once the Gryffindor Quidditch Team. Most of the time, Hermione would ignore Draco but occasionally snapped back at him and in their third year, she even slapped him.
In spite of his dislike toward Hermione, Draco was reluctant to confirm her identity when he was asked to do so by his parents and aunt Bellatrix, avoiding even looking at her. As an adult sobered by his wartime experiences, Draco was civil, if not friendly, towards Hermione and her friends.
A Very Potter Musical
Throughout his first two years of Hogwarts, Draco has a particularly serious crush on Hermione. He wanted a rocketship and Hermione. It's not until after Hermione turns him down after her first year when Draco has returned to the past, that he realises that he should move on considering "what a b***** Hermione is". Draco later meets Luna Lovegood in the Forbidden Forest while waiting to catch up to his time.
- Rowling was not in favour of this pairing