The Welsh international has struggled for first-team football with the Baggies.
Chester is now due to hold talks with Aston Villa over a move to Villa Park and could make the move in the next few days.
Aston Villa are looking to improve their defensive options this summer. The club lost Ciaran Clark to Newcastle United recently and the teams defence has been performing badly for much of the past 12 months.
Following defeat to Luton Town in the EFL Cup last night it is clear that Villa need to strengthen their defence and Chester would bring quality and versatility across the board if he did make a move.
Despite struggling to have an impact in the West Brom team since his move from Hull City last summer, the 27-year-old had a good Euro 2016 with Wales and it is this form that has reminded interested teams of his ability.
Villa will be hoping to get the deal done before their first home fixture of the season, against Rotherham United on Saturday.