I'm just curious because I recently read about Machiavelli and Leonardo's plan to divert the Arno so I'm wondering if there is any documented interaction (in person or through writing) between Michelangelo and Machiavelli.
I'm not certain how well researched or historical it is, but there is some interaction between the two men detailed in The Agony and the Ecstasy, a biographical novel about Michelangelo by Irving Stone. Reading that and Stone's research notes about it might be a good place to start.