The 31-year-old has eight caps to his name. but has not played for his country for over three years because of his injury problems.
Pulis has little doubt about the ability of the player, who decided to join Stoke after rejecting a pay as you play deal from Spurs.
"Woody's got an opportunity to play regularly - if he does well he could get called up for England again," Pulis said.
The centre-half only managed to play one match for Spurs last season due to a groin injury and a strain to his abductor muscle.
The former Leeds defender has been included in the Stoke squad for tonight’s Europa League qualifier first leg against Croatia’s Hajduk Split.