Berahino has impressed for the Midlands side this season and came off the bench to score in a 2-0 win over Crystal Palace on Saturday.
However, Clarke is wary of expecting too much, too soon from the England Under-21 international, whose contract is set to expire at the end of the current campaign.
"For Saido, the most important thing is that he continues to develop as a player," said Clarke.
"That is what I am trying to do with him here and I think he is happy to work with me along those lines.
"My own personal opinion is that he is not quite ready for full international football. It is not for me to tell (England manager) Roy (Hodgson) how to do his job, but that is my personal opinion.
"People are trying to push him too far too quickly. Give the boy time to grow and develop."
Born in Burundi, Berahino has represented England at various age-group levels and boasts four goals in three appearances for the Under-21s.
He marked his first West Brom start, in August, with a League Cup hat-trick against Newport County, before sealing victory over Manchester United the following month with his maiden Premier League goal.
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