The striker is set to leave Stamford Bridge after having a transfer request accepted by Blues boss Andre Villas-Boas.
Sam Allardyce: "If Nicolas is available, I'd be massively interested.
"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 (because Anelka will be available on a free transfer in the summer).
"We need to get into the Premier League - and then we'd have a better chance of signing someone of Nicolas' quality."
Graeme Souness came very close to signing Anelka during his time as Newcastle boss.
Then chairman Freddy Shepherd went to Turkey to thrash out a deal put they couldn't agree personal terms.