Long was recently linked with a loan move away from The Hawthorns, before returning to form with the Baggies.
He was back among the goals on Monday, bagging a brace in a 2-2 derby draw with Aston Villa.
Prolonging his stay in the Midlands has now become a top priority, with his current deal due to expire at the end of the season.
West Brom can take up a 12-month option on Long, but would prefer to see him tied down long-term.
Clarke, who has so far seen talk of fresh terms come to nothing, said in the Birmingham Mail: "Shane's performance at Chelsea was one everyone spoke about.
"He got another goal for the Republic (of Ireland) and he showed tonight that when he's on his game he's a player to be reckoned with.
"That first goal was a difficult goal to take. He showed great control and finished it with his weaker foot, not that you'd notice. And he showed great anticipation with the second goal. It's just a shame we couldn't get the three points.
"I've said all along Shane has a big future for us. We will sit down and I'm sure the talks will try to sort that one out."
Clarke is also hoping that discussions with England U21 international Berahino will produce a positive outcome, with a deal close to being completed.
He added: "I felt the contract was almost done.
"As far as I'm aware the club have made him a really, really good offer. There is not much more negotiation to be done. It's a good deal."