We know that Europeans heard about Mansa Musa and the Kingdom of Mali, because Musa is depicted on the Catalan Atlas. He is depicted seated, with a gold crown and holding a gold nugget, with a n inscription describing him as "Rex Melli" and identifying Melli and Timbuktu (or "tombotou"). Musa's hajj was 1324-25, and the Catalan Atlas is produced circa 1375. So, word of his journey had reached Iberia within 50 years. The image of Musa is repeated in 1413 in the Planisphere of caravan routes across the Sahara produced on Majorca.

In the 1400s, we have accounts of Italian merchants and explorers trying to reach Mali from North Africa. We have surviving copies of the letter by Antonio Malfanti about his time in Tuat (now in central Algeria) and rumors his hosts told him about kingdoms to the south. Malfante does not appear to have ever visited Timbuktu or other Malian cities. There is also the account of Benedetto Dei from the 1460s about his travels in the middle east and Africa, where he claims to have visited Timbuktu and describes it (correctly) as a trade entrepot on the desert edge.

However, this information seems to have been kept secret by Italian and Iberian merchants and map-makers. If we take a look at University of Illinois african maps collection (make sure to sort by date), we can see that the earliest maps in the collection, from the early 1500s, no longer depict Thambet/Tombou/Timbuktu, nor Melli. Rather, they seem to be reproductions of Ptolemy's Geographia (from 2nd century AD). It's not until 1560s that we start seeing Tombotu and Melli again.

A possible explanation for this "forgetting" and then re-learning about the cities of West Africa might be that Leo Africanus wrote a manuscript of his memories about the cities and kingdoms of West Africa in 1527, which was published in Italian in 1550, and was translated into French in 1556 and English in 1600.

So, by the time that Rene Caille sets out on his voyage to try and "discover" Timbuktu in 1828, the city had an established reputation as a wealthy trade hub because of Leo Africanus' book. The connection to Mansa Musa appears to have been largely forgotten.

A pretty good journal article that goes into all of this in more depth is "The Image of Timbuktu in Europe Before Caille" by Richard L. Smith in Proceedings of the Meeting of the French Colonial Historical Society Vol. 8 (1985), pp. 12-22