The 33-year-old is currently plying his trade in China for Shanghai Shenhua but has recently been linked with a move back to the Premier League.
Allardyce, who has guided the Hammers to sixth place in the table after the opening 11 fixtures, signed Anelka for Bolton for a then club-record fee in the summer of 2006 and revealed he would like to work with the France striker once again.
"It could interest me, of course it could," he said.
"It would be of interest if that is a possibility financially for us and he wanted to come.
"I have had no conversations with Nicolas' agent or anything like that at this time."