The Reds have set a departure price of around € 30 million, with the price in England seen as unrealistic as Shaqiri values less.
The Spanish team of Sevilla is considering approaching the Kosovar player and has already begun talks with Liverpool.
Football Insider has reported that Sevilla executives have asked The Reds to cut the price of Shaqiri to around 22m euros.
Shaqiri has a contract with Liverpool until 2023, but his departure from Anfield will take place after two years stay.
In addition to Sevilla, there are other teams in the race: Roma, CSKA Moscow, Zenit St Petersburg, Galatasaray, and West Ham United.