The Mirror says Liverpool face competition from Lazio for Shaqiri.
Shaqiri admitted prior to the World Cup that he would be looking for a move away from Stoke this summer and he's set to be playing Champions League football next season.
Liverpool have been strongly linked with Shaqiri in recent months and TeamTalk reported earlier this week that Manchester United had joined their rivals in the race to sign the Switzerland global.
Liverpool FC are thought to be on the lookout for a number of new signings this summer as they bid to build a squad capable of challenging for the title next season.
According to Turkish outlet Milliyet, Galatasaray have convinced the Senegal global to push for a move despite informing him that he will earn less on his return - €2.75m-per-year in fact, a €750,000 decrease on his current pay packet with the Potters.
Regardless, everything seems to be in place for Shaqiri to become Klopp's third signing of the transfer window following the arrivals of Naby Keita and Fabinho.
Shaqiri has had offers from across Europe following Stoke's relegation to the Championship but once Liverpool firmed up their interest his heart was set on moving to Anfield.
Klopp is looking to add to his attacking options and Shaqiri is seen as the ideal extra player alongside the existing Roberto Firmino, Sadio Mane and Mohamed Salah.