The German star moved to Italy in 2018 on a free transfer but is thought to be keen on a move away from Juventus having made just three substitute appearances in Serie A so far.
The 25 year-old was also left out of the Champions League squad by new manager Maurizio Sarri.
Can is attracting interest across Europe and has a reported preference for a return to the Premier League with Man United, reports Tuttosport.
Can is one of seven players linked with a move to Old Trafford in an ‘ambitious revamp’ of the current squad and is a potential replacement should Paul Pogba leave the club.
Earlier this month, Can hit out at Sarri for not giving him chance to impress this season.
“Last season I played a lot. Especially in important games for Juventus. And I also played well there,” he said. “I haven’t had a chance this season.
“But now I think, when I come back to the club, I will get chances again.
“I am definitely grateful to Joachim Low. Because I didn’t play much in the club and he invited me anyway. Nevertheless, he gave me the chance. That’s why I was simply happy that I played again.”