A girl wants to kiss a guy and he says:
I never would've approached you. Take advantage of you?
I'm pretty sure he means he never would have tried to initiate a relationship with her, or "hit on her" as the current slang expression has it.
So he means his love for her is pure?
Students: We have free audio pronunciation exercises.
No, no. He means he thought she was out of his league. But I'm guessing here, without more context - does that interpretation make sense?
Willia: I think I have a crush on you.
Boris: Yeah, I thought you might.
Willia: Is it okay if I kiss you?
Boris: Yeah.
And after they kiss:
Boris: Willia... I never would have approached you.
Willia: Are you a shy guy?
Boris: Yeah.
In this case, I think Boris might perhaps mean that he was simply too shy to approach Willa. Or, perhaps, any girl.
Teachers: We supply a list of EFL job vacancies
Approach simply means 'move near', or 'go up to'.

In many cultures, people like having their private space. If I see someone sitting alone and feel the need to go up to them ( approach them ) I may feel the need to make an apology or excuse.

"I never would have approached you, but I saw that you were reading my favourite book."
It's often used as a way to go up to someone and not say directly that we are attracted to them.
Thank you!