Anelka, who made his Baggies debut in Saturday's defeat by Southampton, spoke to the club's sporting and technical director Richard Garlic on Thursday after being informed of the news.
It was decided the 34-year-old former France striker should be given time off to grieve, although reports he has retired are believed to be premature at this stage.
West Brom had announced on their official website that Anelka has been given permission to miss Saturday's Barclays Premier League clash with Everton on "compassionate grounds".
While Anelka's brother Claude is more widely known as his agent, the Frenchman's affairs are also handled by Manasse with whom it is believed he had a close relationship.
It is understood that West Brom have opted against setting a timeframe for Anelka's return to duty given the nature of his absence, but his future is clearly now in some doubt with both club and player in limbo.
"West Bromwich Albion can confirm that Nicolas Anelka will not be involved in Saturday's game at Everton," read a statement.
"The club have excused the striker from club duty on compassionate grounds."
Anelka joined West Brom on a free transfer in July having completed a loan spell at Juventus when his lucrative move to Chinese club Shanghai Shenhua turned sour.
The well-travelled former Arsenal, Liverpool and Chelsea striker agreed a one-year deal with the Baggies with an option for a further season.
Following his arrival in the Midlands, Anelka stated that he would like to end his career at West Brom, although clearly not in these circumstances if does decide to retire following Manasse's death.
"I think I will finish in England, I'm happy here. I also hope that it will be with this club. I think this is the right club for me," he said.
"I'm 34 years old now and I want to enjoy my football. I hope everything will be perfect."
Anelka first rose to prominence following his £500,000 move to Arsenal from Paris St Germain as an 18-year-old in 1997.
It proved to be one of the shrewdest pieces of transfer business in football history as two successful seasons later he was sold to Real Madrid for £23million.
But it was the start of a nomadic 16 years for a gifted if temperamental player, who has since played for nine further clubs.
Having won 69 caps for France, the end of his international career came when he was sent home from the 2010 World Cup for verbally abusing coach Raymond Domenech.
Anelka later confirmed Manasse's death while expressing his grief through his official Facebook page.
He wrote: "It is with great sadness that I just learned the death of Mr Eric Manasse. Upset by the news of mourning which strikes his family and relatives, Eric will leave a great void in our lives.
"I can't find the words to express my immense sorrow, and I wanted to bring all my condolences to family Manasse after this tragic loss."