It has been reported by the British tabloid that Gallagher is a £7 million summer transfer target for Stoke, who will play in the Championship next season after getting relegated from the Premier League.
Sheffield United and Blackburn Rovers are also interested in the 22-year-old striker, according to the report, although they are claimed to want the English youngster on loan.
According to The Sun, Southampton manager Mark Hughes is in no rush to sell Gallagher this summer.
Good signing for Stoke City?
Gallagher - who earns £40,000 per week as salary, according to Spotrac.com - is a very talented and promising young striker, and the former England Under-20 international would be a good signing for Stoke.
However, investing £7m on a 22-year-old who has played a handful of games for the Southampton first team would be a long-term risks for the Potters, although he could deliver the goods in the Championship next season.
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