This question seems simple, but it’s impossible to give a simple answer to it.

On one hand, fundamentally enlightenment is the realization that there is no one to be enlightened, so if one thinks of himself as an enlightened person, he is definitely not. Enlightenment makes one very ordinary, very mundane, and everyone is everything for such a person is similarly enlightened. Mundane becomes divine, and divine becomes mundane. There is no difference anymore - they are one and the same.

But it doesn’t mean that such a person cannot say “I’m enlightened”. The key to understand why it’s the case is seeing the projection mechanism at work. Saying “I’m enlightened” does NOT mean thinking of himself as an enlightened person. Just like getting angry does not mean thinking of yourself as an angry person, or saying something nice doesn’t mean you think of yourself as a nice person.

There could be a multitude of reasons why a person might say so. Maybe he still have compassion for other beings and wants to help them (a Boddhisatva, in Buddhist terms). Maybe he has no compassion left, but playing a role of an enlightened guru is his job, the way to make a living. So he may write books, give lectures and announce freely. There’s demand for that and he is qualified - what’s wrong with that? Maybe it’s just fun for him to help others, he enjoys the process, even though the desire to help is not there already. Or maybe he’s just teasing you.

You will never know. For a truly enlightened person, it’s not a statement about him, it’s a statement for the listener.

In any event, don’t think about that from the perspective of humility. Both pride and humility disappear in enlightenment. An enlightened person can’t be humble. He may appear humble to you from the outside, but he can’t be humble just as he cannot be proud.