Marshall is impressing on-loan at Sheffield Wednesday.
The Daily Express says Marshall, 20, will be offered a three-year contract extension after impressing on loan with Gary Megson's Owls. He will then be sent back to Hillsborough for the rest of the season to boost Megson's promotion challenge in League One.
Marshall was out of contract in the summer but Potters boss Pulis has moved to tie him down to a long-term deal.
Pulis said: "Ben is a fantastic prospect and it was always our intention to keep him here.
"He's done well at Wednesday and will get good experience there but we think he has a great future at Stoke."