The club's record £5.5million signing is returning to the club after a loan spell at his former side Reading ended with their exit from the Coca-Cola Championship play-offs.
Pulis is hoping the 29-year-old can kick on next season after he failed to score in 18 appearances for Stoke. He wants Kitson to show the kind of form that brought him 10 goals for Reading in the top flight.
Pulis said: "I have not spoken to Dave yet but obviously Reading's defeat was an enormous disappointment for him.
"He will come back as I thought he was unfortunate here. He had a lot of things going on behind the scenes that did not help. We still think Dave is a quality player. If he gets a couple of goals early on next season that could help him.
"He has done it before and done very well in the Premier League. It hasn't worked here yet but that happens with lots of players. Dave will have a fresh start and if he gets a good pre-season under his belt that will help him."