Anelka was granted compassionate leave a week ago following the death of agent and friend Eric Manasse, with the French striker suggesting at the time he could quit the game such were his depth of feelings.
But after being allowed to clear his head, Anelka was back with the club on Wednesday before resuming training 24 hours later, and is now in line to figure for the Baggies in Sunday's game against Swansea at The Hawthorns.
Assessing the situation, Clarke said: "I don't think he ever said to anybody he might quit because all the conversations he had were private and in house.
"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 came in yesterday and told me he was really looking forward to the rest of the season and to helping West Bromwich Albion build on last season. For me, it was great news."
Clarke insists there are no problems with the 34-year-old Anelka's mental state, adding: "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 [Thursday], 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 would likely have missed last weekend's draw at Everton with a shin injury anyway, but Clarke maintains he has recovered.
"I'm not sure he did too much whilst he was away, but he is naturally very fit. His fitness won't be an issue," said Clarke.
Clarke is also poised to give winger Scott Sinclair his first Premier League start for just over 11 months.
Sinclair signed a four-year deal with Manchester City last summer on the back of a £6.2million move from Swansea, but went on to make just 11 league appearances, including two starts.
Starved of football, the 24-year-old jumped at the chance to join the Baggies on a season-long loan last week.
After playing the 90 minutes of Tuesday's Capital One Cup win over Newport, Sinclair is now eager to revive his career.
"At the end of the day I just want to play football," said Sinclair.
"Every player wants to be at a top team, but you get so frustrated when you don't get an opportunity. You build up to nothing.
"With so many good players at City it was always going to be tough to break into the side, but it was frustrating not to get a chance to show the fans what I could do.
"But that is the way football goes, and hopefully I can get my career back on track, and I don't see it as a come down coming here.
"I want to get back to enjoying my football, being happy, and it is better for me to be playing for West Brom every week rather than being on the bench at City."
Sinclair has also had to overcome the scare of a blood clot detected in his shoulder in May which resulted in him requiring surgery and a rib removed.
"That was a shock, a very big shock," added Sinclair.
"I was out for a couple of months after that, so it's not been a good year for me, but hopefully now being here I can get my career back on track.
"I'm getting back my match fitness, enjoying my football and I want to simply play every weekend."