"No player will leave that is contractually with the club unless we feel it is a good deal and the right deal for them," said Rowett.
"That is the most important thing, but on the flip side to that, if players 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.
Liverpool transfer news: Xherdan Shaqiri hint dropped by Stoke boss Gary Rowett (Image: GETTY)
Liverpool transfer news: Xherdan Shaqiri hint dropped by Stoke boss Gary Rowett (Image: GETTY)
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"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."
Bookies across the UK and Ireland have slashed odds on Shaqiri swapping the Bet365 Stadium for Anfield.
And Paddy Power expect the former Bayern Munich and Inter Milan ace to rock up on Merseyside.
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"Liverpool have taken pole position to sign Xherdan Shaqiri, presumably inspired by Champions League conquerors Real Madrid," said spokesman Paddy Power.
"While the Spanish are led by human Ken doll Cristiano Ronaldo, Jurgen Klopp must have targeted Shaqiri because he’s like an action man – in height, at least.
"The diddy winger has an even diddier release clause in his contract, activated by Stoke’s relegation, and we now expect to see him end up on Merseyside."