Anelka is contemplating retirement following the death of his agent.
He has been granted compassionate leave by the Baggies as he weighs up his options, but they are eager to know where he stands.
Were Anelka to hang up his boots, Clarke would be left with little time in which to find cover for a vastly-experienced striker before the summer transfer window closes.
The Baggies manager told the Express and Star: "I'm conscious that time is short and it's something I will be trying to address today (Wednesday).
"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."
Meanwhile, Clarke has also revealed that he will be looking to land another proven goalkeeper before Monday's deadline - with Ben Foster set to be sidelined for up to 12 weeks.
He added: "It's important I have experienced cover.
"Boaz (Myhill) is fit and he was only on the bench last night against Newport because he's only trained for one day.
"Luke (Daniels) came in under pressure at the weekend at Everton and I thought he deserved his chance. I thought he was good and he looked assured.
"I've got those two keepers and I have no problem with running with them but obviously I need cover.
"The next one after them is Jack Rose, who is a really promising young keeper but is not ready. We will look to bring in experienced cover."