The 20-year-old has been linked with a number of leading clubs, including Arsenal and Manchester United, after an impressive start to the season.
After scoring a hat-trick on his full debut against Newport in August he followed that with goals against Arsenal, Manchester United and Palace.
Berahino has also scored six goals in four games for England U21s and Clarke is keen for him to commit his long-term future to the club.
Speaking on Albion's official website, he said: "I'm confident Saido will sign his new deal within the next 24 hours.
"It will be great for him because he's a young boy and he's maybe become a little bit distracted by the fact it's been going on for so long.
"That's been a little negative for the whole situation but there are not too many negatives surrounding Saido this season.
"He's been a breath of fresh air in the squad, he's been a revelation and has made a big contribution to us already.
"When he signs his contract he has a massive part to play for us for the rest of the season."