The Blues finished 19th in the league for number of shots registered, shots on target and chances created, highlighting the need for a creative maestro like Shaqiri to add a bit of star-dust to play in the final third.
Everton and Leicester have also been linked interest in the Stoke ace, who is certain to move on before the start of the 2018/19 campaign.
Liverpool are chasing several high-profile attackers, but Rowett has confirmed if the Reds make a suitable bid for Shaqiri then the club will grant a sale.More news: Sons of Anarchy Actor Alan O'Neill Dies at 47
'I want to put players on the pitch next season that want to be in a different league and understand the challenges of that league.
Shaqiri was one of the few shining lights for a Stoke team relegated to the Championship and the former Bayern Munich man is clearly a wanted man this summer.More news: France plans to ban mobile phones at school
The 26-year-old is now with Switzerland's squad ahead of their World Cup campaign and is expected to play their first game against Brazil on June 17.