An initial £9m bid for Schlupp, 23, has been rejected by the Foxes.
But Pulis is expected to increase his offer for the Ghana international he wants as his left-back at the Hawthorns.
Pulis also faces a battle to prise Clark away from Midlands neighbours Aston Villa.
Villa boss Roberto Di Matteo is desperate to keep the Republic of Ireland international, 26, as he looks to plot an instant return to the Premier League.
West Brom also want to make sure they have a replacement in place as they continue their pursuit of West Ham’s Diafra Sakho.
Baggies goalkeeper Boaz Myhill has agreed a one-year contract extension.