Yes, there was a recent news story that he might choose his successor to be a woman. He might also choose his next successor while he is alive, a big break with tradition. He has also said that his successor will be born outside of China, but he might hold a referendum about whether there will be a successor at all.
Also that he probably won't make any decision about it until he is 90, about 14 years from now.
Certainly a man can be reborn as a woman and vice versa, and you can be reborn in any culture as well as non human forms, in the traditional ways of teaching about reincarnation in Buddhism. However the most important thing in Buddhist teachings rather than the specifics of reincarnation, is to keep an open mind about things you can't see to be true for yourself,.
There isn't quite the Western idea of a soul transmigrating. That some connection continues after you die, there is that idea for sure, also that the things we do in this life have effects beyond the limited horizons we see, in some way or another, usually in the Buddhist teachings expressed using the idea of future lives.
With the Dalai Lama can think perhaps as transmission of a blessing from one life to another or some such. There is no idea that the personality is the same, likes, tastes, or anything like that from one to the next.
If this rather breaks up ones concepts about what one thought it means to be the Dalai Lama that's probably all to the good.