The 27-year-old forward, who formed part of Spain's triumphant Euro 2012 squad, is believed to have attracted interest from the Viola, who are seeking attacking reinforcements.
However, speaking to Spanish radio station Cope, the Andalucians' president Jose Maria Del Nido insisted that the former Almeria ace will not be available on the cheap.
Negredo joined Sevilla in 2009, and has since played over 100 games for the Rojiblancos, scoring 45 goals.
His contract with Michel's side runs until 2016, and it seems only a substantial bid will see him move to the Tuscan outift.
Vincenzo Montella has already raided La Liga this summer, capturing Borja Valero and Gonzalo Rodriguez from Villarreal.