The Della Valle family owns luxury goods group Tod's and, since 2002, the Florence-based club who last season narrowly escaped relegation.
The source said ACF Fiorentina's owner, Diego Della Valle, and Commisso met on Tuesday at Tod's offices in Milan and that a deal could be struck as soon as later on Tuesday or Wednesday.
Italian-born Commisso, owner of the New York's Cosmos and Mediacom chairman, made a failed offer last year to buy a controlling stake in AC Milan.
Commisso did not immediately respond to a request for comment. It was not immediately possible to reach Diego Della Valle for a comment.
(Reporting by Silvia Ognibene, Elvira Pollina; Editing by Mark Bendeich)
