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Stoke made a bid in the summer for the 23-year-old, whose deal expires at the end of the season, while the Baggies made a third contract offer last month.
Potters manager Mark Hughes has said he remains "hopeful" of signing Berahino in the January transfer window.
But Albion boss Pulis told BBC Sport: "This club has looked after Berahino since eight or nine years of age."
Berahino has not played for the first team since 10 September and was sent to a conditioning camp in France to help him lose weight and regain fitness.
"We are interested in him, as a number of other clubs are," said Hughes. "I am hopeful we will be able to get something done."
Former England Under-21 international Berahino's deal at The Hawthorns expires at the end of the season and Albion have been in talks with him since the summer.
Pulis added: "It has to be a two-way situation. We won't sell him unless it is right for the football club. That has always been the situation; we will not sell the lad because it suits him."
Keep up to date with all the Premier League transfers in January as we track and profile all the players leaving or joining a club this month.
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Tony Pulis says West Brom will not sell striker Saido Berahino "unless it is right for the club".