Anelka left the club's training ground on Thursday after being given compassionate leave, granted after the striker learned of the death of his agent.
Initial reports had suggested a bust-up with the club as the reason for his exit, but speaking to the press on Friday Clarke insisted that there was no fall-out.
He did, however, confirm that the Frenchman had mentioned the possibility of retiring.
"There was no big bust up, he didn't storm out," Clarke said ahead of this weekend's clash with Everton.
"Obviously Nicolas lost a close friend and an agent over the weekend - he died suddenly. Nicolas went to Richard (Garlick, technical director) 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 is just a boy who is really quite upset.
"I'm not going to deny that he used that word (retirement) 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.
"He hasn't trained this week (because of a knock). I was preparing the team for Everton without him."
One player Clarke will have available for the trip to Goodison Park is new loan signing Scott Sinclair.
West Brom completed a season-long deal for the 24-year-old on Thursday and Clarke is now eager to see him in action.
"We needed width in team and he can score," the Scot added. "He's hungry and desperate to play this weekend. It's a big year for him.
"We would like another wide player if possible, we have been under-active compared to others (in the transfer window). I'm hoping we will be busy."
