Anelka reported back for training on Thursday, six days after he reportedly considered quitting the game following the death of his friend and agent Eric Manasse.
Clarke, who has held lengthy talks with the 34-year-old, believes that the Frenchman is fit to face Swansea City on Saturday.
"I don't think he ever said to anybody he might quit because all the conversations he had were private and in house," Clarke told Sky Sports News.
"All I said last week was the quit word did come up in conversation. He was in a really bad place. But we did what any club would do - we gave him time to go away and reflect on things.
"He is good. He explained to me the circumstances around his state of mind last week, and they were all good reasons, and now he is fine. He trained this morning, he trained very well, and I've no qualms whatsoever about playing him on Sunday. I need all the good players I can get."
Anelka joined West Brom on a free transfer during the summer.