Jagielka is leaving the Toffees this summer when his current contract expires, bringing to an end 12 years at Goodison Park.
The 36-year-old departs having played 385 times for the Merseyside team and becoming captain. The centre-back also earned 40 caps for England during that time.
Stoke are looking to reshape their squad under manager Nathan Jones. They are hoping that Jagielka’s connections with the club will help tempt him to Staffordshire.
The veteran’s brother, Steve, was a youth player for the Potters during the 1990s. Jagielka himself also trained with them before joining the Blades’ academy.
Surely Sheffield United are favourites for Jagielka?
While the England international does have some links with Stoke, he has even stronger connections with Bramall Lane.
Jagielka came through the United youth system, progressing to the first team in 2000. Over the next seven years he made 247 appearances for his boyhood side.
The last time Jagielka played for the Blades was the last time they were in the Premier League back in 2007. It would therefore seem fitting if he returned just as they do.
Aside from the emotional attachment, that is another key reason Jagielka would surely choose United over Stoke. Unlike the Potters, they can offer top flight football for next season.
That is after earning automatic promotion from the Championship in 2018/19, finishing second behind Norwich City.
The Sun reports that manager Chris Wilder is hoping to add some Premier League experience to his squad and is considering an attempt to bring Jagielka back.
For the player himself, it would be a chance to prove he can still cut it at the top after falling out of favour at Everton. Last term Jagielka made just seven appearances.
He will turn 37 in August and could bow out helping the club where it all began for him.