The Switzerland international is in high demand due to a £13.5m relegation clause being inserted into his contract.
Reports in Shaqiri's Swiss homeland suggest that a number of top-flight clubs are looking to secure his signature, including Southampton, Tottenham Hotspur and Everton.
Shaqiri has now made clear that he does not plan on playing second-tier football next season, putting Prem clubs on red alert.
"It is no secret that I will leave the club," he told Aargauer Zeitung. "I would love to stay in England, I think the league is perfect for me. It's the best league with the best players, but I do not want to exclude anything.
"Everyone wants to compete with the best, that was one reason why I chose the Premier League. And that's why I want to take the next step now.
"I had a very good season and am satisfied with my services, but the best Xherdan? Probably not. I'm disappointed we went down, that is normal, but I need not blame myself. I gave everything for the team, and we resisted the descent by all means, but unfortunately we could not prevent it.
"Nobody wants to go down, of course. But first, there are worse things in life, and secondly, you can learn from such things. You have to draw the right conclusions for the future."
Shaqiri played a direct part in 15 Premier League goals during Stoke's relegation campaign.