Anelka, who moved to the The Hawthorns on a free transfer in July, was granted compassionate leave by the club last Thursday after learning of the death of his agent Eric Manasse.
Ahead of the clash with Everton last weekend, Clarke admitted that the 34-year-old Frenchman - who has enjoyed spells at Arsenal, Real Madrid, Liverpool and Chelsea in his career - had mentioned the prospect of retirement from the game.
With uncertainty still surrounding his next steps, Clarke is eager to meet with the forward again in order to resolve the matter in the near future.
"I'm conscious that time is short and it’s something I will be trying to address today (Wednesday)," Clarke told The Express and Star.
"We have to arrange a meeting as quickly as we can to get it sorted. I have to sit down and speak to Nicolas.
"We have to get in touch with him or he has to get in touch with us to see how he is and where he’s at.
"As quickly as possible, we need to have that chat."
Clarke was dealt a blow during the 0-0 Premier League draw with Everton on Saturday as goalkeeper Ben Foster suffered a stress fracture of his foot, an injury that could keep him out for 12 weeks.
Luke Daniels filled in for Foster in the closing stages, and then played the full game in the 3-0 League Cup win over Newport County on Tuesday.
Boaz Myhill is also available to play in Foster's absence, but Clarke admitted that he is looking to bring in extra cover in goal.
"It’s important I have experienced cover," Clarke added.
"Boaz (Myhill) is fit and he was only on the bench last night against Newport because he’s only trained for one day.
"Luke came in under pressure at the weekend at Everton and I thought he deserved his chance. I thought he was good.
"I've got those two keepers and I have no problem with running with them but obviously I need cover."
