Anelka is set to leave Stamford Bridge after having a transfer request accepted by Chelsea boss Andre Villas-Boas. With the striker linked with a move to Chinese side Shanghai Shenhua, Anelka claimed last week he already has a move agreed when the transfer window reopens in January.
However, Allardyce, who brought Anelka to Bolton from Turkish side Fenerbahce, admits he would love the chance to be reunited with the former France international, although he is yet to approach Chelsea.
"If Nicolas is available, I'd be massively interested," Allardyce told The Sun. "I've not contacted Chelsea and am just looking at the situation with January looming.
"It would be an end-of-season pursuit rather than next month. We need to get into the Premier League - and then we'd have a better chance of signing someone of Nicolas' quality."