The burly Argentine-born front-man has impressed since his move from Roma, prompting the Serie A champions to explore the possibility of a loan move with a view to a permanent transfer at the end of the season.
The Saints paid £13m for the striker just a matter of months ago and are believed to be keen to keep him at St Mary’s Stadium for the long-term.
However, Osvaldo has already hinted that he may be tempted to leave, opening the door for a stunning January exit.
The prospect of playing regularly in Italy ahead of the World Cup may appeal to the 27-year-old, who is desperate to represent the Azzurri in Brazil.
Juve chief Antonio Conte is willing to offer him just that opportunity as he plots for the possible exit of summer signing Fernando Llorente.
Osvaldo is thought to be finding it hard to settle in Southampton and faces a tough task to maintain a starting berth ahead of Rickie Lambert.
Should Southampton fight to keep Pablo Osvaldo?
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