I'm so sorry. How very worrying for you.
The key question I would consider asking him, is a gentle enquiring:
How would your life be better as a girl?
And listen carefully without interrupting or disagreeing to each example he gives and then say something along the lines of.
"I remember being 11. When I was growing up girls were meant to be feminine, pretty and nice. All the time. And boys had to be masculine, confident and strong. All the time. It was so stupid. I really liked X and Y, and I was told I couldn't like those things as I was a girl. But I went on liking/doing them.
It's much better now we have got rid of those silly gender stereotypes.
You can do (repeat things). Boys can do (repeat things)."
My totally non-professional instinct is that there is likely to be something he is unhappy about, and sees becoming a girl as an escape route. But talking about what he wants in his life may help him open up to you a bit more, and possibly identify some coping strategies.
My brother, as a tweenager, thought that girls had it much easier than boys. Lots of friends, who never had big rows, as girls were always nice? They found homework easy. Teachers liked and trusted them more. They were always given the benefit of the doubt by adults, but he and his friends were automatically 'up to no good'.
He doesn't think that now!
These are, of course, just suggestions, it's your child and you know him best.
But, most children enjoy hearing about what their parents did/liked when they were the age they are now. Photos are good here! So if you were passionate about hedgehogs, a pop band, a terrible TV programme etc , tell them about it. It will probably make them laugh which is always a good thing!
Wishing you both all the very best with this.