Is it possible to have a girl reincarnate of Asura and Indra? Though I haven't seen an instance where the reincarnate of Asura and Indra is a girl, I'm still wondering. So the question is, is it possible to have a girl reincarnate of Asura and Indra?
There isn't any mention of any other incarnates in the manga. It's entirely possible since it's simply chakra reincarnating to a different body, however it's unprovable. 

Purely Theoretically: It does seem as though, from what we've seen and what we know of Asura and Indra, that all of his reincarnations would be descendants of them. Indra and his two known reincarnations (Madara and Sasuke) all have been Uchiha (descendants of Indra) and have had the Sharingan. Asura and his two known reincarnations (Hashirama and Naruto) are Senju and Uzumaki, descendants of Asura's clan. This may be because their decedents share similar chakra (Uchiha have the Sharingan, and Uzumaki/Senju have incredible chakra control and chakra reserves). Theoretically, as long as they're a member of one of these clans they can be a reincarnation.