The Wales international is yet to feature this season due to a hamstring injury sustained in pre-season.
Chester has not actually played a competitive fixture for Villa since January, having struggled with a persistent knee injury which kept him out of the club’s charge to win promotion.
He returned for pre-season fully fit but has not been seen since picking up the hamstring problem late in Villa’s 1-0 friendly win at Shrewsbury Town.
“It has been a frustrating one with his hamstring injury but I am hoping he will be back in training during the international break,” explained Smith.
Chester remains highly thought of by Villa’s boss and the latest injury setback has proved hugely frustrating for a player who missed only one match during his first two-and-a-half years with the club, following a 2016 move from Albion.
The 30-year-old now faces a battle to force his way into the reckoning due to the impressive early season form of Tyrone Mings and Bjorn Engels at the heart of defence. Villa also recruited Ezri Konsa and Kortney Hause during the summer.
Chester first sustained his knee injury last November but played through the pain barrier for more than two months due to Villa’s then defensive shortage.
Discussing the injury at the end of last season, he explained: “I felt it was my duty to continue on and being involved.
“I have damaged my body indefinitely, really. It is something I am going to have to manage for the rest of my career.”
Smith also hopes to have Matt Targett (hamstring) and Jonathan Kodjia (ankle) back available when Villa return to Premier League action on Monday, September 16.