Oh dear :(
11 is very young.
I think I would ask him about his feelings, and listen to what he says about them without trying to discuss your own point of view in the first instance. Reflect back to him what you're hearing, clarify what he's saying etc. Let him know you are sorry if he is feeling badly about himself or his body. Give him a hug.
That's enough for an initial talk, I reckon.
It should give you some more info to go on, and to think about before having a second conversation, which could be focused more on your boundaries for him as a minor.
Something like 'I understand that you're feeling unhappy in yourself at the moment. That's really difficult, and I want to help you as much as I can in a way that won't cause you any harm.
See what he wants to happen. Offer what you feel comfortable happening. I asked ds whether he'd like to talk to someone (private, neutral) about it (I said no to gender clinice). I also reiterated that I supported GNC behaviour and presentation - he could be as feminine as he wanted to be, and I would be OK with it.
I drew clear lines on what would not be happening - blockers, hormones, name changes, pronoun changes, gender clinics. Not because i didn't love him and didn't want to help him, but because it was my job as his mum to keep his options open until he was an adult and no longer in my care.
And then, I would do my best to take the heat out of it. Don't debate it, don't argue over it. Don't make it a topic of conversation. Draw him into as many family activities he likes as possible. Encourage non-gender related activity. Throw money at stuff that looks like another possible interest (if you have it...music has been a bit of a life saver here) Stay close. Don't let yourself be alienated from him. Slow everything about gender down as slow as it can get, and focus more on the other parts of his life.
At 11, I'd consider some internet restrictions also. Not huge ones. And not 'because of gender'. (I mean, yes, but don't frame it that way).
I have no experience of dealing with this and schools (we HE) so I'd imagine that's another thing to think about.
Good luck. Don't panic. If he didn't exhibit dysphoria as a child, this is unlikely to be a permanent identity now. He may be having nascent issues with puberty or his sexuality ? If you can find a neutral therapist, that could be a good option for support.
HTH!