The Stoke City winger is expected to leave the bet365 Stadium after he returns from World Cup duty, where Shaqiri has already hit the headlines for a controversial celebration after scoring the winning goal against Serbia on Friday.
It was reported that Liverpool were the favourites for his signature as manager Jürgen Klopp looks to bolster his attacking options ahead of the new season.
But a report from Don Balon suggests that Barcelona will rival the Reds in the hopes of landing Shaqiri after the World Cup.
Barça are said to be evaluating the future of Ousmane Dembélé this summer but recent reports suggest that the France international will remain at the club next season.
The club's hierarchy are, however, eager to bring in competition for places in their attack in a bid to further Dembélé's development. Although Don Balon continues by suggesting that Shaqiri is being eyed as an alternative to second choice striker Paco Alcácer.
A number of names have been floated around but Shaqiri is now believed to be one of Barcelona's top transfer targets, largely thanks to his rumoured £13.5m release clause.
But the 26-year-old has already expressed his desire to stay in the Premier League next season, insisting that he is perfectly suited to life in the top flight of English football.
"I think the [Premier] League is perfect for me," Shaqiri told Aargauer Zeitung ahead of the World Cup. "I would love to stay in England but I don't want to rule anything out. It's the best league with the best players."