With Ben Foster still recovering from a serious knee injury and unavailable until October, the Baggies have Boaz Myhill as their only remaining senior 'keeper, leaving the club searching for alternatives in the transfer market.
Reports - such as those brought to you by HITC Sport - suggest Albion have been in talks with Cardiff over the Scotland international, with Bluebirds boss Russell Slade admitting they may have to sell their highly-rated shot-stopper in order to improve elsewhere.
According to ESPN FC, Pulis said: "He's a good goalkeeper and a goalkeeper we would like to bring in to the football club. The two clubs have to agree and the player has got to agree, it's not as simple."
"We're not one of the big four or five clubs who can go out and say 'they want X amount so we're going to pay that."
"Bo is the only senior keeper we have available so it's important we get a player in."
Marshall impressed during his single season spent in the Premier League with the Bluebirds, which concluded with his inclusion in Sky Sports' Premier League Team of the season, and he is widely regarded as the best 'keeper in the English second tier.
He kept seven clean sheets during Cardiff's top-flight campaign, while averaging 3.49 saves per game - more than any other player in the Premier League; including Albion's Ben Foster and Boaz Myhill.