Anelka is set to leave Stamford Bridge after having a transfer request accepted by Blues boss Andre Villas-Boas.
The Frenchman is thought to have agreed a move to Chinese outfit Shanghai Shenhua and will quit West London when the transfer window reopens in January.
However Allardyce, who worked with Anelka at Bolton, admits he is keeping tabs on the striker's situation, although he concedes he would only move for the 32-year-old on a free transfer in the summer rather than next month.
"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."
Borussia Dortmund hears Wembley Calling and are headed to London for the Champions League final.
adidas has added some color to the Predator line with this new colorway. Released on May 17. Be the first to own a pair.
Ajax has released their away soccer jersey for the 2013/14 season. Get in the Gear.
The Juventus jersey for the 2013/14 was released earlier this week. Be the first to wear the colors of the Old Lady.
The adidas Nitrocharge is the most talked about new cleat in years. It was released on May 15 and will take your pitch by storm.
The new PUMA evoSPEED 1.2 FG. A great new soccer cleat with classic look and first time for PUMA to be on the cleat.
One of the top soccer cleats for control the Nike CTR360 will not let you down on the field in tight spaces.
Chelsea won the Europa League on Wednesday. The Blues defeated Benfica 2-1 on injury time goal from Ivanovic.
Bayern Munich are kings of Germany and hope to be crowned kings of Europe at Wembley later this month!
The Liverpool 2013/14 soccer jersey is available for pre-order. The Reds are eager to compete for silver next season.