The Serie A side are keen to strengthen their defence ahead of the new season, and the 28-year-old Argentine appears to be the latest addition to head coach Vincenzo Montella's squad.
Fiorentina have yet to agree personal terms with the centre-back, but Rodriguez is expected to sign a long-term deal with the Viola in the next few days.
He started his professional career with San Lorenzo, before joining Villarreal in the summer of 2004.
Rodriguez has since become an integral part of the Yellow Submarine's first team, making 246 official appearances for the club, but was keen to move on following their relegation from La Liga last season.
Meanwhile, Borja Valero has completed his move from El Madrigal to the Stadio Artemio Franchi after passing a medical.
The 27-year-old midfielder has signed a four-year deal with the Italian side.
||WHO WILL TOP THIS YEAR'S LIST?