The Hammers' assistant manager, Neil McDonald, admitted that the Frenchman, who played under Sam Allardyce at Bolton, is among a list of "good players" being looked at by the club
The French forward switched the Premier League for Chinese club Shanghai Shenhua last January after being frozen out at Stamford Bridge, however a dispute over pay may see him leave this winter.
The 33-year-old is thought to favour a move back to England, having turned out for Arsenal, Liverpool, Manchester City and Bolton, where he played under current Hammers boss Sam Allardyce.
Furthermore, the east Londoners are ready to send Andy Carroll back to Liverpool after an injury-plagued loan spell, as revealed by Goal.com, thus the Irons may well be in the market for a goalscorer.
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"We are looking for good players and Anelka is a good player," he told the Daily Star.
"He had a fantastic relationship with Sam."
Goal.com also understands that West Ham are now in talks with the Gunners about a potential move for Moroccan forward Marouane Chamakh as they look to strengthen their attacking options.