Shaqiri last week confirmed that he wants to leave the bet365 Stadium following Stoke's relegation from the Premier League last season, with the likes of Liverpool, Tottenham Hotspur and Southampton understood to be interested in his signature.
The Switzerland international reportedly has a £12m relegation release clause in his contract, but Rowett insists that the Potters will not sell the 26-year-old on the cheap.
"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," Rowett told reporters.
"That is the most important thing but on the flip side to that, if player's say they want to leave, then I want to work with players that want to be at the club. 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.
"I want players who are committed to Stoke City and if players want to leave I will try and find the best solution to make that happen if that is the case."
Shaqiri joined Stoke in 2015 and has since played almost 100 games for the club.