The Switzerland international is reportedly looking for a move this summer after the Potters were relegated from the Premier League.
The 26-year-old has been linked with clubs from all over Europe, including Galatasaray and Roma.
However there is also significant interest in Shaqiri from England as, according to Swiss newspaper Blick, Everton, Tottenham and Southampton are all chasing him.
The Premier League trio have been made aware of the winger’s desire to move away and they are exploring the possibility of a deal.
Shaqiri is said to want his future sorted before Switzerland kick off their World Cup campaign on June 17 against Brazil.