West Brom are hoping to sign another goalkeeper before the end of the transfer window.
The Baggies have been linked with both stoppers already this summer, but with just over a week to go before the window closes, Pulis wants to ensure a new man is signed.
Boaz Myhill has been taking to the field for the opening two games of this campaign, with Ben Foster out injured, and he has failed to impress.
He struggled in the opening weekend defeat to Manchester City, and although a clean sheet was kept against Watford, there were fumbles of the ball which could have cost the Midlands side.
Both Marshall and Hennessey are experienced players, who have impressed when given chances in the Premier League, and deals seem possible for both.
Marshall is likely to accept the chance to return back to the top flight if an offer is made, whilst Hennessey looks to be behind both Julian Speroni and Alex McCarthy in Alan Pardew’s plans.
Pulis has confirmed that enquiries have been made into the purchase of both goalkeepers, and with little time left before the transfer window closes, it would come as no surprise to see him make a concrete approach for one of the stoppers in the coming days.