The Germany international can leave Anfield for free next summer if he doesn’t sign a new contract with the Reds.
Juventus have been linked with the 23-year-old and are monitoring the situation ahead of a potential swoop.
And Italian outlet Tuttosport say Manchester United and Chelsea are also interested in Can.
Bayern Munich are the final side who could make a move for the midfielder.
It may seem unlikely that the Liverpool man would move to rivals United but unless the Reds tie him down to a new deal they won’t be able to stop him.
Loris Karius, Ovie Ejaria, Danny Ings and Jon Flanagan (left to right)
Antonio Conte is keen to bolster his midfielder ranks, despite signing Danny Drinkwater from Leicester on deadline day.
Chelsea missed out on Everton star Ross Barkley and are still short on numbers in the middle of the park.
Can has been impressive for Liverpool so far this season, starting all three of their Premier League matches.
The midfielder also starred in the second leg of the Reds’ Champions League play-off win over Hoffenheim, netting twice at Anfield.
Can will look to continue that good form when Liverpool take on Manchester City at the Etihad this Saturday.