The England Under-21 international has broken into the Baggies team this season with some eye-catching performances - and scored in Saturday's 2-0 victory over Crystal Palace.
There have been suggestions that other clubs are monitoring the young forward closely, and Clarke has urged West Brom bosses to secure his services on a long-term contract.
Talks have been held and Clarke is confident that Berahino is ready to commit his future to the club.
"We are in negotiation with his representatives and if I was the club I'd get it done as soon as possible," said Clarke.
"He's hungry and he wants to play. This contract is important but it's not the most important one he'll ever sign, that's further down the line.
"I think he is happy to work with me."
Clarke was delighted with West Brom's perseverance following their win over managerless Palace.
"They were difficult conditions, for both sides, but I thought we did more than enough to deserve the win," he told Sky Sports.
"We started well and got control of the game. We spoke about starting well and early on it looked like it was going to be a long afternoon for Palace.
"The most important thing is that we came away with three well-earned points."