Anelka, 34, only signed for the Baggies this summer but sensationally walked out of training on Thursday after telling technical director Richard Garlick and first-team coach Clarke he no longer wanted to play.
His agent, Eric Manasse, died earlier in the week and Anelka is understood to have spent two days considering his future in the game.
Anelka's exit on Thursday led to reports of a fall-out, but Clarke denied this was the case, while confirming the player had been given compassionate leave while he decides his future.
Clarke said at his Friday morning press conference: "Obviously Nicolas lost a close friend and an agent over the weekend - he died suddenly. Nicolas went to Richard (Garlick) on Thursday and indicated that he wasn't in a good place.
"I went in and had a very brief chat with him, and he wasn't in a good place. So the club have decided just to give him a bit of time to go away and think about it and get himself in a better place for the future.
"Really, that is as much as there is to tell on the situation - it wasn't dramatic, there was no big bust-up, he didn't storm out of the training ground. It is just a boy who is really quite upset."
Asked directly if Anelka had mentioned quitting, Clarke added: "I'm not going to deny that he used that word in the conversations we had with him. But we've given him time to go away and think about it and I don't think we could do any more in the circumstances as they were."
Anelka revealed Manasse's death while expressing his grief through his official Facebook page.
The former Arsenal, Real Madrid, Paris Saint-Germain, Liverpool, Manchester City, Bolton and Fenerbahce striker wrote: "It is with great sadness that I just learned the death of Mr Eric Manasse. Upset by the news of mourning which strikes his family and relatives, Eric will leave a great void in our lives.
"I can't find the words to express my immense sorrow, and I wanted to bring all my condolences to family Manasse after this tragic loss."
West Brom have been managing the situation, granting compassionate leave and giving him as much time as he needs following the bereavement.
But Anelka, who had said he would retire in England after joining the Midlands club after brief spells at Shanghai Shenhua and Juventus, appears to have decided that there is no point in continuing his playing career, which has been marked by turbulence since his controversial £500,000 move from PSG to Arsenal in 1997.
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