The 31-year-old is highly regarded at Villa, and is club captain - but is keen to find time on the pitch ahead with the 2020 European Championships approaching this summer.
The Welshman is out of contract at Villa Park this summer, and famously played through a serious knee injury under former boss Steve Bruce when injury struck the club's back line during their time in the Championship.
He had feared he'd played his final game for the club during his lengthy spell on the sidelines.
He did however feature under Dean Smith earlier this season, and has been included on the bench regularly over recent weeks.
Chester joined Villa in 2016 from West Brom, becoming a key player as Villa battled in the second tier to eventually earn promotion last season.
Stoke currently sit 20th in the Championship, five points clear of the relegation zone and 16 points from the play-offs.
The Potters had been previously linked and were reportedly close to a move for the defender in the summer of 2018, but following Villa's purchase by Wes Edens and Nassef Sawiris - a departure was ruled out.