First, I assume you know that the next Dalai Lama is chosen as a small child? So the question is, how likely is it that the next Dalai Lama will be a girl child?
He has said himself that, if the Tibetan people decide to continue the institution of the Dalai Lama, then he could be reborn as a girl.
So anyway, rest of this is by way of background.
I'm going to start by answering from the point of view of assuming that the Dalai Lama can indeed direct his rebirth in some sense - so that it is not just a choice made by his companions after he dies. That is what Tibetans believe at least. So, let's run with this and see what the implications are.
In the past things were difficult for female teachers in a traditional society, which is why there are fewer Buddhist nuns and fewer Buddhist female teachers. But still, there are many of both including many female Buddhist teachers.
If you believe in the capability of some of the Buddhist teachers to direct their rebirths to some extent - then is perhaps not too surprising if most teachers choose to be reborn as men, because it is easier to teach in a traditional society as a man.
Perhaps that is why all the reincarnations of the Dalai Lama to date were men as with many other tulkus.
Though there have been some women tulku lineages apparently where all the tulkus were women Women in Buddhism
Today, when it is relatively easy for women to adopt many of the same roles to men in society. including teaching, and can also move reasonably freely and safely throughout society, similarly to a man, then seems no practical reason why the Dalai Lama or other teachers shouldn't choose to be reborn as a woman. So, it's a change in society that makes it easier for a Dalai Lama to be a girl.
Perhaps the Dalai Lama is hinting that this might happen?
That leaves a question though, what does "choose" mean here?
The whole thing about rebirth in Tibetan Buddhism or Buddhism generally is tricky, what it means, as it is easy to try to fit it to Western ideas and turn it into something it is not.
There is no idea of a "soul" in the Western sense to be reborn. That is the main point of distinction between Buddhism and some other traditions with reincarnation such as Hinduism and some Christian reincarnation traditions such as Anthoposophy, etc.
It's more a continuing stream of action from previous to future lives.
So what exactly does "Choose" here mean, when there is no continuing "same person"? Probably not really how we'd think of choice, as in choosing a new suit of clothes or some such.
I'm not the one to answer that properly :). But part of it is that they are called to their new birth by compassion.
At any rate, whatever I say I'll surely get it wrong :).
Just to alert you that anything we say here is going to be an approximation only, is hard to say exactly what is meant by "the previous Dalai Lama was reincarnated as so and so". There is some strong connection of inspiration and blessing and activity for sure from the one life to the next. They are not at all expected to be similar in personality.
For instance the sixth Dalai Lama was a great poet, was not a monk, had many women lovers, and his poetry is much admired to this day. And didn't have a great deal of inclination towards Buddhist scholarship.
The current Dalai Lama passed his "Geshe" degree at a young age, surprising everyone with his keen mind and his erudition. Is a monk of course. And as far as I know, is not noted for his poetry.
You could hardly have more different personalities than the present Dalai Lama and the sixth Dalai Lama.
Anyway whatever, certainly in Buddhist teachings, anyone can be a woman as easily as a man, as you pass from one life to the next, as well as also animals and other creatures too.
But in another sense, it is a great mystery what happens when you die. It may be a bit hard to be a Buddhist fully if one is totally sure that it is the end of everything when you die, However, it is probably good if one is a Buddhist to have an open mind about it.
If one doesn't know for sure what happens when one dies, as is surely usually the case, is good to recognize that.
In Buddhist teaching is no great virtue attached to asserting your faith in things that you can't see to be true for yourself. Instead the teachings encourage an open mind, dropping fixed concepts about things, and seeing for yourself.
The Buddha's teachings just suggest that it is interesting to direct your attention in a particular way to look at things you take for granted and would probably never think to look at or question without his hints.
So that leads to a more open ended approach where it is good to recognize that, for instance, you don't know what happens when you die.
And - is often forgotten, but there was a first Dalai Lama. And after that - they found a way to find his successor, who somehow continued the same inspiration. Not the "same person" but a blessing / inspiration connection.
So, it's like that. Not whether the Dalai Lama will take rebirth - according to Buddhist ideas, he continues in some form, until he reaches Buddhahood (unless he is already, which you could say of anyone). And then Buddhas also can continue once enlightened - the historical Buddha continued to teach for many years after he reached Nirvana. But Buddhas can also enter paranirvana which means there is no further rebirth in the cycle of existence though beings in Samsara can continue of course to be inspired by them - as modern Buddhists are inspired by the historical Buddha.
So anyway - he can continue to take rebirth whether or not his next rebirth is the Dalai Lama. The question rather is whether or not the line of inspiration as the Dalai Lama, which started with the first Dalai Lama, should continue - and - that's not a line of inspiration that can be continued just by appointing someone, like a president, or by birth, like a royal family. Rather it continues through this process of inspiration passing from one birth to another through continuous stream of awareness. Which most people and countries don't recognize as a possibility - or in Buddhist countries, - they recognize it as a possibility but most countries they don't try to find past and future rebirths - and the Buddha himself discouraged it - in general.
But in Tibet, they have this system in place where they feel you can recognize an inspiration like this, which in some sense is due to choice by the previous Dalai Lama of where to take rebirth. So nobody else can legislate for that - it is his own choice that has to be followed as that is what makes the lineage of inspiration meaningful for them. Otherwise it doesn't have this inspiration of the Dalai Lama. That's why the idea of the Chinese that they could appoint their own Dalai Lama or Panchen Lama for the Tibetan people has little support amongst Tibetans.