Forgiving someone shows one’s compassion. Asking for forgiveness shows that you recognize your mistakes, and that you resolve not to repeat them in the future.
Now to say, ‘Only if he/she asks me for forgiveness will I forgive them’, this is of a lower form of forgiveness.
The highest form of forgiveness is to realize that the other committed a mistake out to ignorance, and having a sense of compassion for them.
Forgiving others with a sense of compassion is the best for of forgiveness. Cultivating this sense of forgiveness in oneself is a mark of being noble in character.