Liverpool have made their interest in the player known, who has a £13.5 million release clause as the club was relegated from the Premier League.
Liverpool are confident that they will sign Swiss worldwide Xherdan Shaqiri this summer, according to a report in The Guardian.
Liverpool have already bolstered their midfield options this summer with Naby Keita and Fabinho, for £52.75m from Red Bull Leipzig and £43.7m from Monaco respectively, and had lined up a £53m move for Nabil Fekir until a medical raised concerns.
The Switzerland global is now on holiday, having helped his country reach the last 16 of the World Cup. Liverpool got lucky last season in that their front three - Roberto Firmino, Sadio Mane and Mo Salah - remained fit and healthy for the majority of the campaign, but their lack of depth was exposed during the Champions League final, when Salah departed injured.
The winger, who played at Inter Milan and Bayern Munich before joining Stoke, scored seven goals for the club last season.
His side take on League Two outfit Bury on Saturday before a midweek game against Blackburn Rovers.
Barnsey too is excited at the idea, calling it an "excellent" signing for the club.