Trust me I'm a manager and I have received many noise complains including loud speaking on phone, music, phone rings... I would pay attention to that if as manager I find it hurting to team performance, I have even asked staff not to type aggressive on their keyboard! after all I don't know how reasonable is your manager but that would ruin your relationship.
Assuming that's not an option for you, and if you are not certain how the person would react or it may turn this it to an argument or big fight, you can write them an email explaining this.
And if you want to be very friendly with them, get them a drink or food or snack by surprise! this would break the notion that are you in for a fight.
I would personally try to listen to soft music with headphone not to bother about the keyboard or noises from environment. although it can be distracting.
Last word: being able to work in any environment is a must in current age.