Crystal Palace have also been linked with a move for the Italian star.
Sturaro is being earmarked by Southampton as a potential replacement for Victor Wanyama, who continues to be linked with a move away from the club.
However it would appear that the Saints and Palace are unlikely to sign the player. Tutto Mercato Web are reporting that Juventus have absolutely no desire to sell Sturaro this winter - along with Simone Zaza and Daniele Rugani.
The report states that Juventus want to keep their young Italian talents at the club for their long-term future.
The 22-year-old falls into that category and it seems that Southampton and Palace have missed out on the player.
Sturaro has played 16 times for the Turin club this season and he has scored one goal. It seems that the Bianconeri have big plans for the Italian under-21 international.