The Italian side are reportedly keen on the Colombian international.
According to Gianluca di Marzio, Fiorentina have already made first contact with Aston Villa over a move for Carlos Sanchez.
The Italian side are looking to add a midfielder to their squad this summer as they build ahead of the new season.
Manager Paolo Sousa is particularly keen to improve his defensive options and that has led him to pursuing a deal for Aston Villa man Sanchez this summer.
Aston Villa's Carlos Sanchez wearing a protective mask
The Italians are reportedly keen to get a deal done quickly to try and steal a march on several other clubs who are also interested in the Colombian international.
Aston Villa's Carlos Sanchez in action with Newcastle's Siem de Jong
The report fails to name a potential asking price at present; although it is likely Villa would want to recoup much of the £4.7 million they paid Elche for his services when he joined in 2014.
It is also unknown whether Villa are interested in a sale, with Roberto di Matteo already facing up to the prospect of losing Idrissa Gueye as he nears a move to Everton.
New manager Roberto Di Matteo during the press conference