It isn't clear what you're talking about exactly, but for nonfiction, sometimes you need permission to use lengthy passages from another writer's work, and sometimes you need no permission at all to use an entire work. Read fair use law. It's pretty clear on when these things apply.
In other words, only the editor at the publishing house when you want to submit the work can answer this question. Period. But I can say this, never in my writing life have I asked for permission to quote anyone, and I never will. Nor has any editor asked me to do so.
If you mean quoting what someone says publicly, then you never need permission. If you mean what someone says in private to you, you still don't need permission. If you did, journalism would not exist, nor would any book or article that said something negative about the subject of the writing.
In both cases, if you ask permission, you will probably be told no for anything that's negative. If you receive permission, you will probably have to pay for it. Neither is necessary.