The Frenchman is considering whether to retire from football following the recent death of his agent.
Clarke is now eager to meet with the 34-year-old to decide whether he needs to find cover before the end of the transfer window.
"We have to arrange a meeting as quickly as we can to get it sorted," the Scot told the Express & Star. "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."
Anelka joined West Brom on a free transfer over the summer after a brief spell with Chinese side Shanghai Shenhua.