If - as has been suggested - this impressively characterised head in medallic profile of a black man wearing a bandana refers to the heraldic device [impresa] of the Pucci, a Saracen's Head (also the name of many an English pub!), it would make the panel ineluctably 'Florentine'. However, if it were heraldic in origin, it would normally have been disembodied, with an ornamental truncation of the neck and set in - and most likely carved in one with - a recognisable form of shield. Furthermore, the bandana of the Pucci's device should bear the capital letters 'T T T', the initials of their Latin motto, 'Tempore Tempora Tempera' (Time is a great healer). These replaced the similar shapes of three hammers formerly symbolising their proud, ancestral membership of the Stonemasons' and Carpenters' Guild in the city (Pietra e Legname).
Constant allies of the Medici during the Renaissance, the Pucci were among the families called upon by Cosimo the Elder as a means of indirectly pursuing his own political interests - trusted Medici allies from the Pucci family included Puccio Pucci, who provided Cosimo the Elder with money to improve his living conditions when imprisoned in 1434, prior to being exiled to Venice. By the date of this relief, circa 1500 the prestige of the Pucci had risen even higher, within the international ambit of the Roman Catholic Church, producing within a few decades no fewer than three Cardinals, Roberto, Lorenzo and Antonio. Until 1559, the Pucci continued to be trusted figures in the Medici's ducal and then grand-ducal court [Wikipedia]. There is however no clue to connect this relief with any specific member.
Otherwise, the way in which the clothed portrait bust 'grows' up from the sharp lower border and the very convincing characterisation of the Moor might be taken to suggest that it is a portrait, real [or imaginary, in the sense of a known person from antiquity, perhaps transmitted on a coin or medal obverse]. In this case it does not have to be Florentine in origin, but perhaps north Italian - maybe a product of the Lombardo workshops in Venice [where in the maritime environment actual black men were common - sailors, merchants, pirates etc.: some are even depicted as engaged, nearly life-size statues wearing turbans on the façade of a palace in Venice].
It might therefore be an actual portrait of some distinguished and recognisable black man, who happened to have particularly pronounced features. The turned collar of his heavy cape recalls that enveloping the shoulders of Plato in a marble relief depicting the philosopher - paired with a facing one of Aristotle - in the Bishop's Palace in Trento. They are held to be by the great north Italian sculptor, Vincenzo Grandi (1493-1577). A similar intensity of expression is to be seen in the present moor, indicated by the linear creases in the skin at the back of the neck and on the forehead.
Dr Charles Avery, Cambridge January 2017
 Francesca de Gramatica, in Mina Gregori [ed.], In the light of Apollo: Italian Renaissance and Greece, exh. cat., National Gallery - Alexander Soutzos Museum, Athens, 2003, n. 1.23: 55 x 46 cm.