The 26-year-old centre-back, who is out of contract at Sevilla next summer, has been linked with a move to Arsenal and Liverpool.
But according to his agent, Ariel Kiperszmid, his Premier League suitors could face competition for the 6ft 5in defender's signature from four Serie A clubs.
Kiperszmind says Sevilla turned down offers from Germany and Russia for Fazio in January and are expecting more at the end of the season.
"In January the club rejected offers from Germany and Russia but in the summer they could be looking at making millions of Euros," Kiperszmid told tuttomercatoweb.
"There are four Italian teams interested in him and Serie A could be a good destination for him, but there are also admirers in England.
"Fede could play for one of Europe's top teams."
Kiperszmind says the defender, who joined the Spanish club's B side in 2007, is eyeing a fresh challenge.
"His contract runs out in 2014 and we have spoken about extending it with Sevilla," added his agent.
"However, his future is probably away from Sevilla because he wants to experience something different."