Saints boss Mark Hughes is looking to raid his old club to improve his attacking options at St Mary's this summer, viewing Shaqiri as a player who can improve a frontline which struggled to find the back of the net at times last season.
The Switzerland international has informed the Potters he wants to leave following their relegation and has attracted plenty of interest from Premier League clubs with Tottenham and Everton both understood to be keen.
The 26-year-old has a £12 million release clause in his contract and Southampton are ready to pay that to get their man.
They are not alone in willing to pay that sum though with reports claiming Tottenham are also prepared to meet the terms in his Stoke deal.
While both clubs are ready to step up their interest in Shaqiri, they will need to bide their time with the playmaker having made it clear he wants to focus on Switzerland's upcoming World Cup campaign.