Fazio joined Tottenham from Sevilla in 2014, but the Argentinian defender struggled for form in England and ended up spending the second half of last season back at his former club on loan.
It now looks like Roma are leading the race to sign the defender, but there is no deal in place just yet according to their manager Luciano Spalletti.
"The deal is not official yet, but we are keen to bring Fazio to Rome," Spalletti told reporters.
"Signing him would give us some extra options in defence.
"He has important characteristics and won the Europa League with Sevilla. He might not have played much in England, but he has experience, is mentally strong and is a good player.
"We are keen to see him in action for Roma".