The Italian club lost Immobile to Borussia Dortmund earlier this week and could now look to partly replace him with a move for Uruguayan international Ramirez.
Ramirez who was one of Southampton's first major purchases upon arrival to the Premier League two seasons ago, has not progressed as much as both the team and the player would have liked and could be leaving the side during the Summer.
It is believed that their is interest from a few sides in Italy where he formerly played for Bologna before moving to England but it could be Torino who have the upper hand as they now are armed with some of the fee for losing Immobile.
Now any more concrete interest at this point in time would solely depend on the next manager of the club after Southampton lost their coach to Tottenham.
Ramirez made 18 appearances in the EPL last season with just one goal and three assists made over the course of the campaign.