Shaqiri has a release clause in his contract which the Daily Telegraph claim is in excess of the £12million figure which has been widely reported.
Despite some impressive displays for the Potters last season, Shaqiri was unable to help the club avoid the drop as Stoke slipped back down to the second tier of English football after a prolonged stay in the Premier League.
Stoke City will be playing in the Championship this season, but it's becoming increasingly unlikely that Xherdan Shaqiri will be joining them there.
A move to Anfield would make Shaqiri the Reds' third signing of the summer following the arrival of midfielders Fabinho and Isaac Christie-Davies.
He is now on holiday after representing Switzerland at the World Cup, helping them to the last 16 where they were beaten by Sweden.
But the issue is that Liverpool have a policy of fining clubs who loan their players but then do not play them for a set amount of games.
Klopp, meanwhile, remains keen to add at least one more attacking midfielder to his squad this summer. Fekir, in any case, is still with France at the World Cup and would not be due to return to action until early-August.