The 20-year-old has made a name for himself this season off the back of a string of impressive performances, scoring the winner as West Brom beat Premier League champions Manchester United at Old Trafford in September.
That goal propelled Berahino into the spotlight and prompted Albion to open negotiations on an improved contract with the England Under-20 international to warn off any potential interest from rival clubs.
Clarke is confident that talks will be concluded soon, as he said: "It's getting closer.
"The club have been discussing the deal with Saido's people for a number of weeks now.
"It's getting close and it will take care of itself."
Clarke's own future has been in the headlines this week after it was revealed that he is due to down and discuss a new deal, with his current contract set to expire at the end of the season.
Ahead of Monday's Midlands derby with Aston Villa, the Scot insisted he is keen to stay at The Hawthorns, although he is no rush to sort out the finer details.
He added: "It's not a big issue for me because I think there is a lot of football to be played.
"We have a big game on Monday night against our local rivals, which we’re looking forward to.
"The contract situation for me will take care of itself. We have a number of games over December and January.
"It's a busy, busy time and, when we get time, myself and the club will discuss the way forward.
"As far as I know, talks were always planned for New Year.
"I'm happy with the situation and the club is happy – and that should put everybody's mind at rest."
