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West Brom are 13/5 with William Hill to beat Newcastle on Saturday
An unused substitute in Monday's 2-2 draw with Aston Villa, the England Under-21 international now appears close to a deal.
"I'm confident Saido will sign his new deal within the next 24 hours," Clarke said. "It will be great for Saido 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.
"The next stage for Saido is to keep doing what he's doing and try and improve.
"He doesn't need to worry where he is in the pecking order because I think I've shown this season if it's the right moment to put him onto the pitch, I've done it.
"He knows exactly where he is in the scheme of things here and how I use my squad.
"When I turn to the bench, if I've got choices to make, Saido has already shown he can be the player I bring to the pitch or the player to start games."
Berahino has made nine appearances in all competitions for West Brom this season, scoring six goals.