Whether The Legend of Zelda: Breath of the Wild would have a female protagonist or not was a polarizing subject, and indeed Nintendo did toy with idea, but as we now know this was not the direction they ultimately opted to go in. Eiji Aonuma shared this information when asked stating:

“So yes, there were rumors like that, and we did discuss as a staff as to what would be possible if we took that route.”

When considering a female protagonist Aonuma and his team actually considered making Zelda the main hero for a change, which would have been interesting:

“We thought about it, and decided that if we’re going to have a female protagonist it’s simpler to have Princess Zelda as the main character.”

But in the end they did not decide to go down this path, and what was the reasoning? I actually find this pretty amusing Aonuma sights the reason behind not using Zelda is what would Link be doing instead:

“…if we have princess Zelda as the main character who fights, then what is Link going to do? Taking into account that, and also the idea of the balance of the Triforce, we thought it best to come back to this [original] makeup.”

He mentions the balance of the Triforce as part of the reasoning and actually this is not that bad to consider, while Link can certainly be a girl himself as part of the Triforce he is the hero and Zelda isn’t. Maybe one day we get a main series Linkle but for now we will just have to wait.