The German has moved into the final six months of his contract at Anfield, meaning that he can now discuss a pre-contract with overseas sides.
Italian champions Juventus are known to hold a long-term interest in the former Bayer Leverkusen man, with some reports in Italy claiming that personal terms have been provisionally agreed between player and club over a potential move.
However, English news outlet 'Sky Sports' reports that the Merseysiders have not given up hope of keeping the Germany international and will sit down with the player this month to discuss terms over a new deal.
The aforementioned source claims that the sticking point in negotiations so far has been Liverpool's unwillingness to put a release clause in the 24-year-old's contract, with the inclusion of such a clause against club policy.
Can recently confirmed that he has yet to make a decision on his future, saying that he is simply concentrating on his football.
Losing the midfielder would come as yet another blow for Liverpool after Philippe Coutinho swapped Anfield for the Camp Nou earlier this month.