Ballard played in the recently concluded season at Championship side Millwall on a season-long loan from Arsenal.
Although the centre-back missed a clutch of games owing to injury at the Den, he still managed to impress.
Stoke, who are looking to push for promotion from the Championship next season, are among several sides that scouted the Arsenal starlet while he was playing for Millwall.
And the Gunners are aware of growing interest in their academy product and are prepared to listen to offers for his services, as he is keen on playing first team football on a regular basis.
Arsenal are open to selling the centre-back but want to include a first-option or buyback clause in any deal for him.
In addition to the Potters, Millwall are keen on signing Ballard on a permanent basis, while Queens Park Rangers, Burnley, Cardiff City and Sheffield United are among his admirers in the Championship.
It remains to be seen whether Stoke will push to land the in-demand defender in the summer.
