That contention has turned up in a lot of places online, but is harder to find in scholarly literature. One article I ran across that stated it as having happened had space for the footnote citation for it, but actually left the note field blank and failed to cite the original source.
The closest thing to original source material I've been able to find is a quoted response to a question posed to Richard Sherman in a NY Times review of the Broadway adaptation of The Jungle Book in 2013. In it, Sherman says that he and his brother were thinking of Louis Armstrong when they wrote "I Wanna Be Like You", but there is *no* mention of whether or not Walt actually wanted to hire Armstrong for the role.
https://www.nytimes.com/2013/06/23/theater/the-jungle-book-comes-to-the-stage.html
Wikipedia and several other internet sites, including a long Reddit "Today I Learned" thread cite this NY Times article as the source of the story that Walt Disney wanted to cast Armstrong, but careful reading of the article and the statement accredited to Sherman reveals that the article does not actually say that at all. At most, it implies that the Shermans thought Armstrong would be a good casting choice, but that some unidentified "they" in a production meeting objected on the basis that the NAACP would protest.
Interestingly, this book presents an argument that Louis Prima was Walt's one and only choice for the part: PAULY, J. J. (2005). Taming the Wildest.
Afterlife as Afterimage: Understanding Posthumous Fame,
2, 191.
I suggest you read both of these sources and also ask your university reference librarians for help on questions like these; helping students with searches like this one is a large part of their jobs, and they will have access to otherwise paywalled scholarly materials that may shed light.
