The Italian central midfielder played in important role in Torino's ninth-place finish in the 2014-15 Serie A season which saw them finish ahead of giants AC Milan.
Reports suggest the Saints have tabled a bid worth something in the region of £6million.
However, issues with such bid could arise due to the player being co-owned by both Torino and Inter Milan. The two clubs are rumoured to be bidding for his full services between them. Both Benassi's availability and price could depend on the outcome of this.
These reports come as Saints boss Ronald Koeman looks to bolster his midfield with Morgan Schneiderlin's impending departure looking increasingly likely.
Benassi made 37 appearances for Torino in all competitions last year, notching three goals in the process.
Rumour Rating - 6/10: it looks like the press are linking Saints to anyone who plays in central midfield at the moment. In my personal opinion, I think the co-ownership could put a halt to this deal if the reports are true.