The German international has been in excellent form this season, helping his side to move into contention for the Bundesliga title.
His consistent displays have caught the eye of Brendan Rodgers, who is known to be on the lookout for forward-thinking additions next month.
The Northern Irishman’s side have made an excellent start to the campaign, but the ex-Swansea chief is aware that he may need to sign one or two players to keep their title challenge on track.
A wide-man is a priority, with Sam seen as an ideal solution.
Teenage ace Raheem Sterling is currently in fine form, but Rodgers sees a reliance on such a young player as a potential problem.
A number of sides are interested in the Sam, 25, but Liverpool are hopeful that their relationship with Bayer Leverkusen manager Sami Hyypia – who enjoyed the finest years of his playing career at Anfield – may aid their hopes of sealing a deal.
FC Basel winger Mohamed Salah is another option, with some reports suggesting that a £7m deal is close to completion.