Liverpool FC, though, could be forced to wait until after the World Cup as Shaqiri prepares to feature in the major tournament in Russian Federation.
Jurgen Klopp, the Liverpool manager, knows Shaqiri from his time in the Bundesliga and is considering a bid as he looks to strengthen his squad.
"No player will leave the club that is contractually with the club unless the club feel it is a good deal and the right deal for them", said Rowett, who was speaking at his first press conference since taking over at Stoke this summer.
Kilauea's eruptions are very different to what's happening in Guatemala. Here's how
One More Child's Vice President Andrew Tattrie said members have been keeping the organization up to date with what's happening. Guatemala's seismology and volcanology institute is warning of new volcanic flows on the western slope of the Volcano of Fire.
Shaqiri and KAA Gent's £10m-rated Moses Simon have both been touted as potential wide additions with Liverpool short on pace and quality out wide behind their two starters and Alex Oxlade-Chamberlain, capable of filling in on the flanks, expected to be out with injury until November.
The Anfield club are close to securing a deal worth around £53m for Lyon play-maker Nabil Fekir having already recruited Fabinho from Monaco for £43m last month.
We'll have to see how things progress but competition for Shaqiri will increase if he impresses for Switzerland at the World Cup so Liverpool or Tottenham may want to act fast if they want to sign him.