The 24-year-old Frenchman made 25 appearances for Villa after joining from Nantes in an £8million deal two years ago, but spent last season on loan at St Etienne following relegation from the Premier League.
And the former France Under-21 player now looks set to join the Viola, with the club tweeting a picture of him undergoing a medical.
French outfit St Etienne had been keen to make Veretout’s deal permanent, but sporting director Dominique Rocheteau said in quotes reported by football-italia.net: “We know him well as a man and a footballer, but frankly we were surprised and disappointed by his conduct.
“He didn’t respect the word he had given us and the agreement we had with him.
“His arrival had all been organised, but he then told us he wanted to go to Fiorentina.
“His choice is a sporting one. Now we’ve discovered that we weren’t his first choice.”