The Potters are believed to be expecting an exodus of their top players following the club's relegation from the Premier League.
Shaqiri made 36 league appearances for Stoke last season and scored eight goals but could not prevent the Staffordshire outfit from dropping into the Championship.
The 26-year-old has been linked with clubs from all over Europe, including Galatasaray and Roma, but Swiss newspaper Blick claims that there is also interest in the player from England.
The report suggests that Premier League trio Spurs, Everton and Southampton have been made aware of the Switzerland star's desire to move away and are exploring the possibility of a deal.
Shaqiri has made 92 appearances for Stoke since his 2015 move from Inter Milan, scoring 15 goals and registering 15 assists.