I'm sure some response relevant to this has come up before, and a moderator will surely show up at some point to direct you to a better answer than I have time to provide here, but in the interim, this is what I can provide you:

The regions encompassed by the empires of Ghana, Mali, and Songhai were literate, using Arabic script and language, and even adopting Arabic script to local languages at least by the height of the Malian empire. Cities like Timbuktu, where Sankore University (madrasha is more accurate, but was comparable to a medieval European university combining theology and secular education; also, technically there were three universities), Gao, and Jenne Jeno, still posses tremendous libraries of medieval texts. There are two major reasons we don't have a lot of the kind of written history you speak of though, and it has a lot to do with local values around oral vs written history, and around outside scholarship of the currently extant libraries.

West Africa has a long tradition of oral historians known at griots. Griots formed a special occupational class and like blacksmiths or potters, if your father was a griot, so to would you be, and your children, and so on (traditionally only men, I think, but I would have to confirm). Oral histories and stories would be passed down through the family. Griots were an integral part of courtly and elite life in Medieval Saharan/Sahel West Africa. They were the keepers of history, voices of morality, and other culturally important traditions. Their function in society was varied, but relied on their refined skills at memorization, word-play, and poetic innovation. Where westerners tend to think of "history" as something objectively true, factual, and immutable, in West Africa (and in fact other parts of the world in history) "history" was something flexible, meant to be used to inform the present and influence future action. One role of the griot in places like the royal court were to shape retellings of oral histories to address contemporary matters; in a sense, making history "relevant" to current questions, ferreting out our adding moral lessons and whatnot. Griot often were, in essence, advisers and wise men who used their oral skills and the mysticism surrounding their skills to sway current and future actions with the idea of respecting tradition and upholding cultural norms and values, even if that meant adding, removing, or twisting historical facts. In such societies, history was not seen as a static thing, but something that could be reshaped again and again to address current concerns. That said, such stories today are still hugely valuable to archaeologists (and I assume historians, but I'm an archaeologist). The Epic of Sundiata, for example, recounts the founding of the Malian empire and existed solely as an oral history until it was written in the 20th century, but has been hugely influential in archaeological research even if many aspects have been mythologized, exactly as the Homeric epics of the Trojan War. (Griots had other roles, such as as praise singers, but that's beyond the current question). While there were certainly no were-women and magical instruments, the information on ethnic and dynastic politics, couched in more relatable terms of individual people in many cases, conveys a wealth of historical facts that have been supported from alternative sources.

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On the other hand, it seems written records were valued for other aspects of society. The libraries of the Inland Niger region contain a lot of scholarship on things like science, medicine, theology, philosophy, etc... mostly built on broader Islamic scholarly trends. Unfortunately for western scholars, many of these libraries were privately held and kept secure from sticky-fingered colonists, raiding religious fundamentalists, and, until recently, foreign scholars. There have been huge efforts to digitize these libraries, but far less to translate and publish them. However, again, for these scholars it seems recording local histories was far less important to them than other forms of literary pursuits. "History" as we think of it seems to have remained largely the domain of oral historians, and, to reiterate, West African views of history and its recounting were much different from the notions of history produced by post-Enlightenment Western scholars. History was, in a sense, a living thing subject to shift with the needs and desires of current societies, not something to be fossilized for posterity (though there is a whole debate to be had on how even current written has and still does this in Western society).

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Edit: I just noticed your use of "hearsay" in the title. I know you said English is not your first language. This is a pretty dismissive term and fundamentally misunderstands the nature of oral history in oral societies. Oral histories in many societies that rely on them often contain a wealth of true and verifiable information, though as I try to argue, "objective" truths are not always the intended purpose of oral history or what is valued in the society at large.