The 21-year-old has scored 12 goals in the Premier League this season to help the Baggies ensure survival.
Pulis believes the forward should snub interest from some of the Premier League’s top teams in order to stay and continue his development under him at the Hawthorns.
“I think the kid should stay,” Pulis said. “I have said that to him that he should stay.
“I think he is enjoying his football, he has enjoyed it with us, I think he has a better rapport now with everybody around the football club.
“I think he could do with another 10 years at West Bromwich Albion!”
The 18-goal star has failed to score in his last nine games ahead of Monday’s visit of Premier League champions Chelsea.
Berahino’s last strike came in the 2-1 defeat at Aston Villa more than two months ago despite Albion sealing their top-flight survival this month.
He is expected to be part of the England Under-21s squad for Euro 2015 this summer and Pulis admits he has been impressed with how Berahino has handled himself this season.
“I worry a little about him but it is not a physical burnout, it is a mental burnout as much as anything else,” he said.
“He’s a young lad. Brown Ideye has been injured, Victor Anichebe has been injured and we have only had three strikers this year and the kid has taken all the weight on his shoulders.
“It has been remarkable how he has handled it and the way he has done it and he deserves a hell of a lot of credit.
“I am more concerned with the amount of games he has played, even on Saturday at Newcastle we gave him a little bit of a rest.
“He is going to be playing in the Euros this summer. The lad has played and been involved in more games this year than he has ever been involved in, so it has been a little bit of a drain for him in some respects.”
Watch West Brom take on Chelsea live on Sky Sports 1 HD from 7pm on Monday.