The French striker, who played under the 58-year-old at Bolton Wanderers, is currently with Chinese club Shanghai Shenhua, but is reportedly eager to return to the Premier League.
"It could interest me, of course it could," the Daily Mail quotes Allardyce as saying.
"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.
"His professionalism and dedication was why he was such a good player and we never had problems at Bolton at the time he was with us. He was the difference - he was the reason we went into the top end, the top four, rather than the top eight."
Anelka joined Shanghai in January 2012.