Amavi made the switch to L'OM from Aston Villa this week but the 23-year-old has now confirmed he could have moved to Serie A instead.
The left-back says there was concrete interest from Fiorentina and his former Villa team-mate Jordan Veretout, who joined La Viola this summer, tried to convince him to make the move to Italy.
Amavi was also linked with Nice, where he came through the youth system, but he says there was no firm offer from Les Aiglons.
"Have I been contacted by other clubs? Yes, especially Fiorentina. It was concrete," Amavi told La Provence. "They called me and introduced me to the project. There are some players I know who left there, like Jordan Veretout and Valentin Eysseric. Veretout even tried to get me to Florence, but I chose OM!
"The fact that I was in contact with Nice for a possible return? Nice did not propose anything. But if your training club calls you, it can be interesting."