The Reds are in the market to improve their attacking options in the 2018 summer transfer window ahead of the new Premier League campaign.
The Merseyside outfit have funds to spend after Philippe Coutinho in a £142m deal from La Liga giants FC Barcelona in the 2018 January transfer window.
Liverpool FC pulled out of a deal to sign France and Lyon playmaker Nabil Fekir after concerns about the 24-year-old’s knee problems.
Shaqiri has impressed at the World Cup with the winner in a 2-1 victory over Serbia to help his country reach the round of 16.
The Reds have been linked with a £12m swoop to sign the Switzerland international from the Potters in the current transfer market.
Sunday Times reporter Castles believes Southampton will rival Liverpool FC for the Swiss star’s signature this summer.
“He will have offers from other clubs. There is interest from Southampton,” Castles told the Transfer Window podcast.
“He might consider because he might play regularly. He’d love to go to Liverpool and try to secure a first-team place.”
Liverpool FC haven’t won the Premier League title in their history but the Reds finished in second place in 2002, 2009 and 2014.
Shaqiri was unable to help Stoke avoid relegation but the Switzerland international isn’t expected to remain at the Britannia Stadium.
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