The bid is thought to be worth £5m with add ons but Russell Slade is adamant that he wants to keep his No.1 and that it's now in the hand of Cardiff City Chairman Mehmet Dalman.
Russell Slade told Wales Online “Yes, West Brom have made an enquiry, there is definite interest there. It’s with the chairman now.
“I would not want to lose a player of David’s quality.
"He is an integral part of what we have done.
"He is a talent and is a sought after player every summer."
Marshall is suspended for the first three matches of the season after he received a straight red card on the last day of the season against Nottingham Forest.
Sky Sports have reported that a fee is close to being agreed between the Bluebirds and the Baggies.
"Sometimes a player is difficult to replace and David falls into the category.” Russell Slade continued.
Marshall's first game of the season will be Blackburn, away, on 18th August, until then his understudy Simon Moore will be starting.