The striker was recently named the Potters' Player of the Season in what was his first campaign with the club.
Pulis now believes that the 31-year-old should be included in Roy Hodgson's 23-man party when it is announced on Wednesday.
"I'm just hoping and praying he gets selected because I know it's what he wants and, also, I think he should," he told Sky Sports News.
"Roy Hodgson has to do what he has to do, but, for me, I would have Crouchy there and able to come off the bench if required.
"In big tournaments you need game changers. Peter might not be going there to play every single game, but one thing is for sure, when he comes on, he can change them."
Crouch picked up the last of his 42 England caps against France in November 2010.