Anelka left Chelsea for Shanghai Shenhua a year ago but local media in China have reported that the French striker's management is in talks to cut short his contract due to unpaid wages.
The much-travelled player, now 33, has reportedly been earning more than $300,000 a week in China.
"He's a player that is of interest to anybody. He's finishing in China so he's available," said Redknapp, whose side hauled themselves off the bottom of the Premier League last weekend with their first win of the season.
"It's what you can do, whether you can afford these players, what they're looking for, whether they are reasonable, whether you can deal with them, whether you feel they can do the job that you want.
"Whether we can afford to get anywhere near, I'm not sure," he told reporters ahead of Saturday's game at Newcastle United.
Redknapp said QPR's Malaysian chairman Tony Fernandes had contacts with Anelka's management but cost was the key.
"It depends how expensive the whole package comes to. If it's in reason, he's a player that could certainly improve your team," said the manager.
Redknapp said QPR would not be forced into panic buying by their league predicament.
"At this time of the year in our situation you spend your whole time looking through lists and lists of players," he said. "You get agents calling you up about players and 95 percent of them are useless and the odd five percent might be OK.
"Teams think they can screw you into the ground because you are desperate. You might ring up about a player worth 3 million pounds and they might ask for six because they know you don't want to get relegated.
"We won't fall into that trap though and if you can't get the right player then we will sit tight."
Looking forward to Saturday, Redknapp said it was time QPR had their first away win of the season although Newcastle were a strong team at St James' Park.
Goalkeeper Julio Cesar and defender Jose Bosingwa will both miss the trip due to back problems while Kieron Dyer and South Korean Park Ji-sung are also injured.
Rangers also announced on Friday that technical director Mike Rigg, who joined from Manchester City to link up with then-manager Mark Hughes, was leaving the club. Hughes was sacked in late November. (Reporting by Alan Baldwin; Editing by John Mehaffey)