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 Barclays 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."
Anelka was seen as a marquee signing for Wanderers when he was signed from Turkish side Fenerbahce and his form at the Reebok Stadium earned him a big move to Chelsea a year and a half later.
Allardyce, who has yet to see big-name summer signing Andy Carroll score for the Hammers, believes Anelka transformed his Bolton side into a team that could challenge at the right end of the table.
He said: "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."
Much has been made over the years of Anelka's demeanour on and off the pitch but Allardyce reckons the perception of the former Arsenal and Real Madrid forward is off the mark and hopes the family man could be tempted to head back to London.
Asked whether he ever had a problem with Anelka's questionable temperament Allardyce said: "He never was like that in his entire time I had him.
"He was disappointed I left, when he came and played for me I had him at a very, very good time - probably at the height of his career, I would think, because he had matured into a dedicated professional.
"I think he has always been dedicated but he got sidetracked by certain situations through his younger days but he learnt from that, his experience across Europe.
"He had a girlfriend, who is now his wife, and his family and I think that has matured him - I think Nicolas has still got his family here in London, I don't think they moved out to China."
One stumbling block for a potential deal would come if Anelka refused to take a drop in his wages as he is currently reported to be earning around £250,000 a week in China.
He has also been linked with a return to Liverpool or a move to fellow strugglers QPR but all three clubs would be hard pushed to fork out the sort of money the Frenchman is currently bringing in from Shenhua.