Clarke was sacked earlier this month after a run of six games without a win that had seen West Brom slip into the lower reaches of the Premier League table.
The Midlands club have since drawn their last two games under the stewardship of interim boss Keith Downing, but sit only a point above the relegation zone in 15th place.
Downing is to take charge of West Brom's next game with West Ham on Saturday, however, a permanent appoint appears imminent, with former Real Betis coach Pepe Mel thought to be among the frontrunners for the post.
"We have identified suitable candidates to work within our existing structure," West Brom sporting and technical director Richard Garlick said in a statement on the club's official website.
"This is a confidential process and it is inevitable there will be speculation about whom may be under consideration.
"We are now progressing through the interview and short-listing stage. We plan to make an appointment at the earliest opportunity but our primary concern is recruiting the most suitable individual.
"We are grateful for the professional manner in which Keith Downing, the coaching staff and the players have approached the last two games.
"Keith remains in charge for tomorrow’s (Saturday) game at West Ham United and until an appointment has been made."
