Several media reports said on Saturday that the sponsor has demanded he is dropped against Everton or else they will immediately cancel their deal.
Anelka is being investigated by the Football Association (FA) for making the gesture after scoring the first of his two goals in a 3-3 draw at West Ham in the league on December 28.
The quenelle, invented by French comedian Dieudonne, has drawn widespread condemnation in Anelka's homeland and from anti-racist and Jewish groups in England who have demanded the player be banned.
Anelka, 34, has played in every league game since making the alleged gesture. He promised no repeat but did not apologise for his actions.
Zoopla has made no public comment on the issue but Marketing Week magazine quoted company sources over the Albion ultimatum.
A spokesman for the club 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."
Last week the Jewish Chronicle newspaper accused the FA and West Brom of failing to deal with the matter quickly enough while Kick It Out anti-racism campaigners said they were "very frustrated" with the time taken to reach a conclusion.
Spaniard Pepe Mel, new coach of 14th-placed West Brom, will be in charge for the first time on Monday.
($1 = 0.6081 British pounds)
(Reporting by Mike Collett; editing by Tony Jimenez)
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