Bolton have completed the capture of former Crewe striker Max Clayton on a three-year contract.
Felix Magath has been sacked by Fulham, with Kit Symons taking over as caretaker manager.
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."