The Hammers manager worked with the Frenchman briefly during his time in charge of Bolton and would relish a reunion as he seeks to continue his newly promoted side's Premier League momentum.
|WEST HAM LATEST
|3/1||William Hill offer 3/1 for Kevin Nolan to score in a West Ham win over Stoke City
"It could interest me, of course it could," he told The Sun. "I think Nicolas still has his family in London so it would be of interest if that's a possibility financially."
Anelka earned a reputation for his sulky behaviour during his various spells in English football but Allardyce dismissed the tag.
"He never was that in the time that we worked together," the Hammers boss added.
West Ham lie seventh in the Premier League, with a tie against Stoke City to be played on Monday evening.