He said via The Birmingham Mail: "We are in negotiations with the club and the player. It's obviously subject to a medical and personal terms."
Should it happen, Chester would represent Aston Villa's fifth signing of the summer, following Tommy Elphick, Pierluigi Gollini, Aaron Tshibola and Ross McCormack - who cost £11 million - to Villa Park so far.
Chester started all six of Wales' matches during Euro 2016 as Chris Coleman's side defied the odds to reach the semi-final stage of the tournament in France this summer.
The 27-year-old, who joined West Brom from Hull last summer, would certainly add a solidity to Aston Villa's defence - and they need it.
Di Matteo's side shipped three goals in a League Cup first-round defeat at Luton Town this week and there is a sense that they will need to bolster their defensive options if they are to stand any chance of winning promotion back to the Premier League.
Aston Villa manager Roberto Di Matteo watches from the dugout