Shaqiri has made no secret of his desire to leave the Potters following their relegation from the Premier League, with Liverpool quickly emerging as the favourites for his signature.
The Telegraph reports that the Reds have now begun official negotiations over a move and plan to trigger the 26-year-old's release clause, which is understood to be more than £13m.
The exact details of Shaqiri's release clause are unknown, but the Switzerland international will be available at a cut price and Jurgen Klopp has identified him as one of his main transfer targets this summer.
The Anfield outfit have held a long-standing interest in Shaqiri, having initially been linked with him when he left Inter Milan to join Stoke in August 2015.
The attacker, who was part of Switzerland's squad at the World Cup, could become Liverpool's third signing of the summer after Fabinho and Naby Keita.