The Daily Mail says the former France international is considering his future in the game after a tragedy in his personal life which led to dramatic scenes at the club's training ground.
Officially, Anelka has been granted compassionate leave for an indefinite period after his agent, Eric Manasse, died earlier this week.
But it is understood that the ex-Chelsea and Liverpool forward, now 34, cleared out his locker, taking his boots with him before informing the club of his decision to call it a day.
According to sources within the club, Anelka had been considering his position some 48 hours before communicating it to his employers.
It seems that Manasse's death hit the player hard and, after collecting his personal effects, he went to see West Brom's sporting and technical supremo, Richard Garlick.
He told the club's director that he no longer wanted to play football and was quitting the game.
Garlick attempted to persuade Anelka to stay but he left soon afterwards. It is not yet clear whether the player spoke to head coach Steve Clarke.
Anelka later confirmed Manasse's death while expressing his grief through his official Facebook page.
For the big stories and the banter follow us on Twitter: @tribalfootball