The Scot has been playing for the Development side during pre season as he is suspended for the first three games of the new campaign.
Simon Moore has been in goals for the first team.
Reports from the Midlands say Tony Pulis is looking at Marshall to challenge Boaz Myhill for the No.1 shirt at The Hawthorns.
Sky Sports Jim White has further fuelled the reports with the following tweet
West Brom close to agreeing a £5m deal for Cardiff City and Scotland goalkeeper David Marshall #SSNHQ
— Jim White (@JimWhite) July 31, 2015
Marshall has been linked to both Everton and Liverpool sice City's relegation in 2014. He is the current Scotland No. 1 keeper and has Premier League experience.