The Potters' relegation has triggered Shaqiri's clause, muted to be around £12 million, leaving a number of Premier League clubs circling around the international.
Tottenham Hotspur, Everton and Newcastle United are all reported to be interested in the winger, who Liverpool are considering bringing in to add depth to a star-studded frontline that contains Mohamed Salah, Roberto Firmino and Sadio Mane.
Strength in depth was considered a big concern for the Reds last season, the likes of Adam Lallana and Danny Ings thought to represent a large drop off in quality when brought on for one of the starting three.
Signing Shaqiri would go some way to bridging that quality gap from starters to back-up's, whilst offering a cheap option that allows Liverpool to concentrate the bulk of their funds elsewhere.
Gerrard makes moves at old club
Playmaker Ovie Ejaria has also made a move up to Scotland, he joins Gerrard's new team on loan for a year immediately after extending his Liverpool contract.
It's thought that Gerrard could seek to take one more Liverpool prospect up to Rangers with him for next season, striker Rhian Brewster amongst those linked.