Roberto Martinez is focusing on Everton's final 11 games rather than talking about the World Cup or players' contracts.
Arsenal forward Lukas Podolski has denied claims that he was offered in a swap deal for Schalke's Julian Draxler.
Reports continue to suggest the Frenchman is set to leave Chinese club Shanghai Shenhua in January after a pay dispute.
England is thought to be the most likely destination for Anelka, who has spent successful spells at Arsenal, Liverpool, Manchester City and Chelsea during his career.
The 33-old striker also played for Bolton between 2006 and 2008, when he worked under Sam Allardyce and a reunion could now be possible at West Ham.
"We are looking for good players and Anelka is a good player," said assistant manager Neil McDonald in the Daily Star.
"He had a fantastic relationship with Sam."