The suggestion follows Anelka's controversial 'quenelle' gesture made during Albion's 3-3 draw at West Ham on December 28, which the Football Association is currently investigating.
When contacted by Press Association Sport, spokespersons for both West Brom and Zoopla, a property and house prices website, declined to comment on Marketing Week's report.
John Simpson, West Brom's head of communications, said: "West Bromwich Albion will be making no further comment until the Football Association has concluded its investigation, and the club its own internal inquiry, into the matter."
Zoopla's head of communications, Lawrence Hall, added: "We are not commenting at this stage."
It is understood Zoopla is far from happy with West Brom's decision to continue to play Anelka despite the furore surrounding the gesture, which has been declared by some to be anti-Semitic.
Zoopla is co-owned by a Jewish businessman, Alex Chesterman.
The reported claim is that Zoopla will pull out of its deal with Albion, which currently has another six months to run, should Anelka play in Monday's Barclays Premier League match against Everton at The Hawthorns.
It is believed West Brom, whose new head coach Pepe Mel tackles his first game in charge against Everton, are still intending to play Anelka.
The issue has overshadowed the club for the last three weeks, and unsurprisingly they have now called on the FA to bring it to a close.
The FA was criticised this week by Kick It Out for its initial silence on the matter, and for not acting quickly enough, with the campaign group calling for "an urgent decision".
The FA has so far made no comment other than to state an independent expert was aiding its probe, and there would be no further update until January 20 at the earliest.
There is a possibility Anelka will be handed a lengthy ban should he be charged and found guilty, denying the club a key striker for a phase of their bid to avoid relegation this season.
With the Baggies selling Shane Long to Hull for a fee that could rise to £7million, the potential loss of Anelka would further weaken Mel's forward options, and with the clock ticking towards the closure of the transfer window at the end of the month.
West Brom's sporting and technical director Richard Garlick said of the Anelka issue, before the sponsorship issue emerged: "There are investigations ongoing, and while they are we won't make any comment."
Pressed on the matter, Garlick added: "People can speculate there is a turn of events where we might be two strikers down.
"It would help everyone for that investigation to be over as soon as possible, and the FA have given their statement about how quickly they will do that."