The Torino midfielder is not set to head to St Marys this summer.
It was reported by Sky Sports Italia that Southampton were keen on the player, who had previously been owned by Inter Milan.
Now his agent Francesco Romano is quoted by Tutto Mercato Web as stating:
"He is a player they like, but it was never formulated into any financial offer."
So it seems that whilst Southampton do like the player, they are not ready to make a move for the player – who can play in midfield or defence.
The Italian under-21 international recently came to the fore at the UEFA Under-21 European Championships in the Czech Republic. He scored a brace against England in the final group game in the tournament.
Why would Southampton need him?
Well the obvious reason would be as a replacement to Morgan Schneiderlin.
The French international is being linked with moves to the likes of Manchester United, Liverpool and Tottenham among many, with Southampton struggling to keep hold of him.
With European football to contend with Southampton will need more options across the pitch, although it looks like Benassi will not be one such recruit.