The Premier League duo were closely linked with a move for the Germany international earlier this summer by the Daily Mail.
Gündoğan was expected to remain at Borussia Dortmund after signing a contract extension with the club last month.
However, TuttoMercato claim that following the injury to Sami Khedira, Juventus have set their sights on the 24-year-old.
Juventus won the Italian Serie A title last season with a 17 point gab between second placed Roma and reached the UEFA Champions League final.
The Bianconeri’s were defeated 3-1 by Barcelona in the final which was played at the Olympiastadion in Berlin. Juventus take on Udinese in their opening game of the 2015-16 season.
Gündoğan wrapped up the season with five assists and three goals in 33 appearances in all competitions.