The Frenchman has not featured for West Brom since coming off in the 25th minute of last month's 4-3 defeat at Aston Villa with a shin injury.
Anelka could be unavailable for even longer as he will have a personal hearing with the Football Association early next week.
The 34-year-old was charged over his controversial 'quenelle' celebration following a goal in the 3-3 draw with West Ham in December.
Anelka contested the charge and has continually insisted the sign is anti-establishment, though critics say the gesture is racist and anti-Semitic.
Though he has been training, Mel confirmed he would play no part at The Hawthorns this weekend.
"Nicolas had his first training session on Thursday, so it's impossible that he plays against Fulham," he said.
"He is out. He's fit and he's good after the injury but he hasn't trained enough.
"As for the other thing (FA charge), sorry, I'm the head coach only. I'd like the better outcome for Nicolas and West Brom but I respect the FA and its decision is good for me.
"For me, what's important is that Nicolas was injured and it wasn't possible for him to play in recent matches. In the future, I don't know."
West Brom are currently 17th, and are outside of the relegation zone only by virtue of goal difference.
But Mel remains confident of beating the drop, adding: "I am sure (we will stay up), of course.
"West Brom will be playing in the Premier League, I'm sure. But more important for me is that the players think that too. I'm the coach, I don't play."
